クラスを使用Canvas Path Pointして、Google マップにポリラインを描画できます。また、参考のためにこのリンクを見る必要があります  。
List<Overlay> mapOverlay;
  protected onCreate(Bundle savedInstanceStae){
     //Do the rest stuffs
      mapOverlay = mapView.getOverLays();
      mapOverlay.add(new MyOverlay());
     }
class MyOverLay extends Overlay{
       public MyOverlay(){}
       ArrayList<GeoPoint> points = new ArrayList<GeoPoint>();
       public void draw(Canvas canvas,MapView mv, boolean shadow){
            super.draw(canvas,mv,shadow);
         Paint mPaint = new Paint();
         mPiant.setColor(Color.RED);
          //set strokewidth and all function depending upon you how you want to give a look                 
          //on Polyline.
        GeoPOint gp1 = new GeoPoint((int) (lat * 1000000.0), (int) (lon * 1000000.0));
        GeoPOint gp2 = new GeoPoint((int) (lat * 1000000.0), (int) (lon * 1000000.0));
        GeoPOint gp3 = new GeoPoint((int) (lat * 1000000.0), (int) (lon * 1000000.0));
       GeoPOint gp4 = new GeoPoint((int) (lat * 1000000.0), (int) (lon * 1000000.0));
     points.add(gp1);
     points.add(gp2);
     points.add(gp3);
     points.add(gp4);
     //Then take two points class object:
    Point point1 = new Point();
    Point point2 = new Point();
    Path path = new Path();
    for(int i = 0; i<points.size(); i++){
      projection.toPixel(points.get(i),point1);
      projection.toPixel(points.get(i+1),point2);
      path.moveTo(point2.x,point2.y);
       path.lineTo(point1.x,point1.y);
     }
   canvas.drawPath(path, mPoint);
}