In this paper, an online adaptive control strategy is proposed for the accurate trajectory tracking of quadrotor unmanned aerial vehicles (UAVs) under time-varying model uncertainties and external disturbances. A robust sliding mode controller was developed for the outer-loop position subsystem to guarantee robust tracking performance even under disturbance. For the inner-loop attitude subsystem, an online adaptive controller was designed, which integrated the fuzzy and SMC into one unified system. Critically, its parameters were simultaneously identified and adjusted in real-time. These sub-control systems were then integrated into a unified closed-loop system. Its uniform stability was then analyzed and strictly proofed. Case studies demonstrated the effectiveness of our proposed strategy, along with its superior control performance when compared with several commonly used methods.