In this paper, an unknown system dynamics estimator (USDE)-based sliding mode control (SMC) is presented for quadrotor attitude tracking with the aims of conquering control oscillation problem and achieving great robustness. To enhance the anti-disturbance ability of quadrotors, the invariant manifold-based USDE, with features of simple structure and exponential error convergence, as well as low computational consumption, is introduced to recover the unknown disturbances by basic filter operation and algebraic calculation. Aiming at accelerating sluggish transient convergency in conventional disturbance compensation-based SMC, a novel quadrotor attitude SMC strategy containing a continuous double hyperbolical reaching law (DHRL) is designed, which greatly alleviates control oscillations without sacrificing dynamic response. The dramatical advantage of proposed scheme is that the chattering-free property and fast dynamic response with precise static tracking performance are simultaneously achieved. Meanwhile, all the error signals involved in the closed-sloop system are proved to be bounded by Lyapunov analysis. Eventually, the effectiveness of explored control strategy is illustrated through simulations and experiments.INDEX TERMS Chattering avoidance, sliding mode control, double hyperbolical reaching law, disturbance compensation, attitude tracking, quadrotors.