There are some other posts on this. I had the same problem for many months. I made sure my quad was not twisted, or unbalanced, I fixed it by simply increasing the accelerometer filters on the TAB Attitude>settings. You can do it starting with 5, than 7, than 8, too much is also not good. dont ask me why but after this ( my filter is at 12) my quad starts the flight straight and stays straight.
I saw another problem which was related to the output tab. Make sure your escs are calibrated, and the minimum spinning is set to a flawless rotation of the motors, and the banks are all set to the same speedrate, rapid esc, oneshot...