Aiming at the problems of parameter perturbation and external disturbance faced by quadrotor unmanned aerial vehicles during flight, a novel time-varying adaptive backstepping sliding mode control strategy is proposed. By establishing an integrated dynamic model of attitude and position, an enhanced sliding surface with an integrated term is designed to eliminate steady-state error. On this basis, a time-varying adaptive gain mechanism based on an exponential function is introduced to dynamically enhance the control gain during the disturbance activation period, thereby improving the robustness of the system in uncertain environments. Finally, an extended Lyapunov function is constructed, and the asymptotic stability of the closed-loop system is proved by combining the Barbalat lemma. The effectiveness of the proposed algorithm is verified through MATLAB/Simulink software simulation. The simulation results show that the proposed control strategy can effectively suppress chattering, quickly converge and stably track the expected trajectory under disturbances. Compared with the traditional backstepping sliding mode control (BSMC), the proposed time-varying adaptive backstepping sliding mode control reduces the root mean square error of position tracking by 67.4% and the root mean square error of attitude tracking by 79.4%.