Here is source code of the Program to Draw Driving Route on Google Maps in Android. The program is successfully compiled and run on a Windows system using Eclipse Ide. The program output is also shown below.
Here i start a service in my tracker activity which updates my current location constantly and sends my current location yo my tracker activity which then draws a line between my previous known location and my current updated location by using map.addPolyline() method.

Tracker Activity


package com.example.travelplanner;

import android.annotation.SuppressLint;
import android.app.Activity;
import android.content.BroadcastReceiver;
import android.content.Context;
import android.content.Intent;
import android.content.IntentFilter;
import android.graphics.Color;
import android.os.Bundle;
import android.util.Log;
import android.view.Menu;
import android.widget.Toast;

import com.google.android.gms.maps.CameraUpdateFactory;
import com.google.android.gms.maps.GoogleMap;
import com.google.android.gms.maps.MapFragment;
import com.google.android.gms.maps.model.LatLng;
import com.google.android.gms.maps.model.Marker;
import com.google.android.gms.maps.model.MarkerOptions;
import com.google.android.gms.maps.model.Polyline;
import com.google.android.gms.maps.model.PolylineOptions;

public class Tracker extends Activity {

double latitude;
double longi;
private static final LatLng JLNStadium = new LatLng(28.590401000000000000,
77.233255999999980000);
LatLng JLNS = new LatLng(28.55, 77.54);
private double pLati, plongi, dLati, dlongi;// previous latitude and
// longitude

private GoogleMap map;

private BroadcastReceiver receiver = new BroadcastReceiver() {

@Override
public void onReceive(Context context, Intent intent) {
Bundle bundle = intent.getExtras();
Log.i("Here", "onreceived");
if (bundle != null) {

latitude = bundle.getDouble("lati");
Log.i("Tag", latitude + "");

longi = bundle.getDouble("longi");
Log.i("tag", longi + "");
drawmap(latitude, longi);
}
}
};

public void drawmap(double latid, double longid) {
// draw on map here
// draw line from intial to final location and draw tracker location map

Log.i("Tag", "map");

// add line b/w current and prev location.

LatLng prev = new LatLng(pLati, plongi);
LatLng my = new LatLng(latid, longid);
//map.moveCamera(CameraUpdateFactory.newLatLngZoom(my, 15));
// map.animateCamera(CameraUpdateFactory.zoomTo(10), 2000, null);

Polyline line = map.addPolyline(new PolylineOptions().add(prev, my)
.width(5).color(Color.BLUE));
pLati = latid;
plongi = longid;

}

@Override
protected void onResume() {
super.onResume();
registerReceiver(receiver, new IntentFilter("com.example.mc_project"));
}

@Override
protected void onPause() {
super.onPause();
unregisterReceiver(receiver);
this.onStop();
}

@Override
protected void onStop() {
// TODO Auto-generated method stub
super.onStop();
}

@Override
protected void onCreate(Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
setContentView(R.layout.activity_tracker);
final double src_lati = getIntent().getDoubleExtra("src_lati", 0.0);
Log.i("Tracker_Src_lati", src_lati + "");
final double src_longi = getIntent().getDoubleExtra("src_longi", 0.0);
final double dest_lati = getIntent().getDoubleExtra("dest_lati", 0.0);
final double dest_longi = getIntent().getDoubleExtra("dest_longi", 0.0);

pLati = src_lati;// intialize latitude and longitude here from intent data.
plongi = src_longi;

// & get destination lai and longi. from intent data
dLati = dest_lati;
dlongi = dest_longi;

try {
// Loading map
initilizeMap();

} catch (Exception e) {
e.printStackTrace();
}
Intent loc_intent;
loc_intent = new Intent(getBaseContext(), Getlocation.class);
loc_intent.putExtra("lat", dLati);
loc_intent.putExtra("lon", dlongi);
startService(loc_intent);

}

@Override
public boolean onCreateOptionsMenu(Menu menu) {
// Inflate the menu; this adds items to the action bar if it is present.
getMenuInflater().inflate(R.menu.tracker, menu);
return true;
}

@SuppressLint("NewApi")
private void initilizeMap() {
if (map == null) {
map = ((MapFragment) getFragmentManager()
.findFragmentById(R.id.map)).getMap();
Log.i("Tag", "map");
// draw line b/w intial and final location.

LatLng strt = new LatLng(pLati, plongi);
LatLng end = new LatLng(dLati, dlongi);
Marker start_m = map.addMarker(new MarkerOptions().position(strt)
.title("START"));
Marker end_m = map.addMarker(new MarkerOptions().position(end)
.title("JLN"));

//map.moveCamera(CameraUpdateFactory.newLatLngZoom(strt, 15));
map.animateCamera(CameraUpdateFactory.zoomTo(10), 2000, null);

Polyline line = map.addPolyline(new PolylineOptions()
.add(strt, end).width(5).color(Color.RED));

// check if map is created successfully or not
if (map == null) {
Toast.makeText(getApplicationContext(),
"Sorry! unable to create maps", Toast.LENGTH_SHORT)
.show();
}
}
}

}

Service

package com.example.travelplanner;


import android.app.AlertDialog;
import android.app.Notification;
import android.app.NotificationManager;
import android.app.PendingIntent;
import android.app.Service;
import android.content.Context;
import android.content.DialogInterface;
import android.content.Intent;
import android.location.Location;
import android.location.LocationListener;
import android.location.LocationManager;
import android.os.Bundle;
import android.os.IBinder;
import android.os.Message;
import android.os.Vibrator;
import android.provider.Settings;
import android.util.Log;
import android.widget.Toast;

public class Getlocation extends AbstractService implements LocationListener {

private Context Context;
boolean isGPSEnabled = false;
boolean isNetworkEnabled = false;
boolean canGetLocation = false;
int flag = 0;
Location location;
Notification notification;
Location mylocation = new Location("");
Location dest_location = new Location("");
float distance;
NotificationManager notifier;
public double latitude;
double longitude;
private static final long MIN_DISTANCE_CHANGE_FOR_UPDATES = 40;// 40 meters
private static final long MIN_TIME_BW_UPDATES = 1000 * 60 * 2;

// update location within a time period of 2 minutes

@Override
public void onCreate() {
// TODO Auto-generated method stub
super.onCreate();
Log.i("Tag", "on create");

}

@Override
public void onDestroy() {
// TODO Auto-generated method stub
Log.i("Indestroy", "destroyed");
flag = 0;
stopSelf();
stopUsingGPS();
super.onDestroy();
}

@Override
public int onStartCommand(Intent intent, int flags, int startid) {
// TODO Auto-generated method stub
Context = this;
Log.i("tag", "on start");
mylocation = getLocation(Context);

Double msg = mylocation.getLatitude();
Log.i("my long", msg.toString());

Double dest_lat = intent.getDoubleExtra("lat", 0.0);
Double dest_lon = intent.getDoubleExtra("lon", 0.0);
Log.i("get lat", dest_lat.toString());
Log.i("get lon", dest_lon.toString());

this.dest_location.setLatitude(dest_lat);
this.dest_location.setLongitude(dest_lon);
Log.i("get lon", dest_lon.toString());

return START_NOT_STICKY;
}

protected LocationManager locationManager;

public Location getLocation(Context Context) {

try {
locationManager = (LocationManager) Context
.getSystemService(LOCATION_SERVICE);
isGPSEnabled = locationManager
.isProviderEnabled(LocationManager.GPS_PROVIDER);
isNetworkEnabled = locationManager
.isProviderEnabled(LocationManager.NETWORK_PROVIDER);

if (!isGPSEnabled && !isNetworkEnabled) {
// no network provider is enabled
Log.i("No gps and No Network ",
"No gps and No Network is enabled enable either one of them");
Toast.makeText(this, "Enable either Network or GPS",
Toast.LENGTH_LONG).show();
} else {
this.canGetLocation = true;
if (isNetworkEnabled) {
locationManager.requestLocationUpdates(
LocationManager.NETWORK_PROVIDER,
MIN_TIME_BW_UPDATES,
MIN_DISTANCE_CHANGE_FOR_UPDATES, this);
Log.d("Network", "Network");
if (locationManager != null) {
location = locationManager
.getLastKnownLocation(LocationManager.NETWORK_PROVIDER);
if (location != null) {
latitude = location.getLatitude();
longitude = location.getLongitude();
}
}
}
if (isGPSEnabled) {
if (location == null) {
locationManager.requestLocationUpdates(
LocationManager.GPS_PROVIDER,
MIN_TIME_BW_UPDATES,
MIN_DISTANCE_CHANGE_FOR_UPDATES, this);
Log.d("GPS Enabled", "GPS Enabled");
if (locationManager != null) {
location = locationManager
.getLastKnownLocation(LocationManager.GPS_PROVIDER);
if (location != null) {
latitude = location.getLatitude();
longitude = location.getLongitude();
}
}
}
}
}

} catch (Exception e) {
e.printStackTrace();
}

return location;
}

public void stopUsingGPS() {
if (locationManager != null) {
locationManager.removeUpdates(Getlocation.this);
}
}

public double getLatitude() {
if (location != null) {
latitude = location.getLatitude();
}
return latitude;
}

public double getLongitude() {
if (location != null) {
longitude = location.getLongitude();
}
return longitude;
}

public boolean canGetLocation() {
return this.canGetLocation;
}

@Override
public void onLocationChanged(Location location) {

mylocation = getLocation(Context);
Log.i("Tag", "location changed");
distance = mylocation.distanceTo(dest_location);
Log.i("Tag", "" + distance);
if (flag == 0) {
Intent intent1 = new Intent("com.example.mc_project");
intent1.putExtra("lati", mylocation.getLatitude());
intent1.putExtra("longi", mylocation.getLongitude());
sendBroadcast(intent1);

//Toast.makeText(this, "broadcasted", Toast.LENGTH_LONG).show();
if ((distance) < 600) {
Log.i("Distance", "dist. b/w < 1km");
Log.d("location", "" + distance);
NotificationManager notificationManager = (NotificationManager) Context
.getSystemService(Context.NOTIFICATION_SERVICE);
PendingIntent pendingIntent = PendingIntent.getActivity(
Context, 1, new Intent(Context, MainActivity.class), 0);
Notification notification = new Notification(
R.drawable.ic_launcher,
"You areached ur destination!!",
System.currentTimeMillis());
notification.defaults |= Notification.DEFAULT_SOUND;
notification.setLatestEventInfo(Context,
"You areached ur destination!!", "You areached ur destination!!",
pendingIntent);

notificationManager.notify(11, notification);
Vibrator vi = (Vibrator) getSystemService(Context.VIBRATOR_SERVICE);

vi.vibrate(1000);
flag = 1;
onDestroy();
}
}
}

@Override
public void onProviderDisabled(String provider) {
}

@Override
public void onProviderEnabled(String provider) {
}

@Override
public void onStatusChanged(String provider, int status, Bundle extras) {
}

@Override
public IBinder onBind(Intent arg0) {
return null;
}

@Override
public void onStartService() {
// TODO Auto-generated method stub

}

@Override
public void onStopService() {
// TODO Auto-generated method stub

}

@Override
public void onReceiveMessage(Message msg) {
// TODO Auto-generated method stub

}

}