This paper presents an adaptive fuzzy control scheme for quadrotor trajectory tracking. A fuzzy system is employed to approximate a model based control law developed using backstepping techniques. The adaptive laws for tuning the adjustable parameters of the fuzzy system are derived based on the Lyapunov synthesis approach. The proposed controller yields asymptotic tracking, while keep the stability of the closed loop dynamics of the quadrotor and boundedness of approximation errors. Numerical simulation results are provided to illustrate the good tracking performance of the proposed adaptive control approach.