In this paper, an Adaptive Fuzzy Backstepping Control (AFBC) approach with state observer is developed. This approach is used to overcome the problem of trajectory tracking for a Quadrotor Unmanned Aerial Vehicle (QUAV) under wind gust conditions and parametric uncertainties. An adaptive fuzzy controller is directly used to approximate an unknown nonlinear backstepping controller which is based on the exact model of the QUAV. Besides, a state observer is constructed to estimate the states. The stability analysis of the whole system is proved using Lyapunov direct method. Uniformly Ultimately Bounded (UUB) stability of all signals in the closed-loop system is ensured. The proposed control method guarantees the tracking of a desired trajectory, attenuates the effect of external disturbances such as wind gust, and solves the problem of unavailable states for measurement. Extended simulation studies are presented to highlight the efficiency of the proposed AFBC scheme.