Following track...XTK or whatever.

When I am all finished with everything on the ground, I start engines and take off.After I am over 1000ft, I turn the aircraft in direction of flight path (pink line).My problem is that I'll turn on LNAV, and it will follow it (path, pink line) for a while, then it will start to not follow it and will get like 5 miles of error from the flight path, is that normal?