Move marker with gps in google map android

First of All implement LocationListener in your Activity then

if you need to show only one Marker(update position of Marker), use this :

private Marker currentPositionMarker = null;

 @Override
    public void onLocationChanged(Location location) {

      LatLng  latLng = new LatLng(location.getLatitude(), location.getLongitude());
        CameraPosition cameraPosition = new CameraPosition.Builder()
                .target(latLng).zoom(14).build();

        // mMap.clear(); // Call if You need To Clear Map
        if (currentPositionMarker == null)
            currentPositionMarker = mMap.addMarker(new MarkerOptions()
                    .icon(BitmapDescriptorFactory.defaultMarker(BitmapDescriptorFactory.HUE_YELLOW))
                    .position(latLng)
                    .zIndex(20));
        else 
            currentPositionMarker.setPosition(latLng);


        mMap.animateCamera(CameraUpdateFactory
                .newCameraPosition(cameraPosition));
    }

or if you want to add a new marker every time :

 @Override
    public void onLocationChanged(Location location) {

        LatLng latLng = new LatLng(location.getLatitude(), location.getLongitude());
        CameraPosition cameraPosition = new CameraPosition.Builder()
                .target(latLng).zoom(14).build();

        mMap.addMarker(new MarkerOptions()
                .icon(BitmapDescriptorFactory.defaultMarker(BitmapDescriptorFactory.HUE_YELLOW))
                .position(latLng)
                .zIndex(20));

        mMap.animateCamera(CameraUpdateFactory
                .newCameraPosition(cameraPosition));
    } 

if location was changed rapidly, it would take a couple of seconds for your app to update its location marker

You can use below code to update position of the Marker

public void onLocationChanged(Location location) {

    double lattitude = location.getLatitude();
    double longitude = location.getLongitude();

    //Place current location marker
    LatLng latLng = new LatLng(lattitude, longitude);


    if(mCurrLocationMarker!=null){
        mCurrLocationMarker.setPosition(latLng);
    }else{
        mCurrLocationMarker = mGoogleMap.addMarker(new MarkerOptions()
                                .position(latLng)
                                .icon(BitmapDescriptorFactory.defaultMarker(BitmapDescriptorFactory.HUE_RED))
                                .title("I am here");
    }

    tv_loc.append("Lattitude: " + lattitude + "  Longitude: " + longitude);
    gMap.animateCamera(CameraUpdateFactory.newLatLngZoom(latLng, 15));

    //stop location updates
    if (mGoogleApiClient != null) {
        LocationServices.FusedLocationApi.removeLocationUpdates(mGoogleApiClient, this);
    }

}

You don't need to clear map every time. You can do it by Marker object that is returned when adding Marker to Map. Hope it will help you.