To implement fast tracking control of large angle maneuvering of quadrotor UAVs， a nonsingular fast terminal sliding mode controller with more compact structure is designed on the SO(3)， which eliminates the singularity of Euler angle description and the problem of local linearization.The modified reaching law can accelerate the system approaching speed when far from the sliding state， and eliminate the chattering effectively.The stability of the controller is proved by using the Lyapunov stability theory.The simulation results show that the attitude is tracked quickly with high precision and low chattering.