The Quadrotor unmanned aerial vehicle (UAV) exhibits high agility and maneuverability, making it widely applied in scientific research, including military and civilian applications. However, during UAV flight, external disturbances and parameter uncertainties are present, which significantly impact the tracking performance of quadrotor UAV. To address this issue, this paper proposes a trajectory tracking method for quadrotor UAV based on Adaptive Backstepping Sliding Mode Control (ABSMC). This method introduces the backstepping technique in the construction of the sliding mode controller and incorporates an adaptive switching gain through a differential iterative approach in the design of the backstepping method. This adaptive sliding mode control effectively suppresses the chattering phenomenon of the sliding mode controller. To validate the effectiveness of the proposed method, stability analysis of the system is conducted using the Lyapunov function. Finally, simulation experiments are conducted to compare the Sliding Mode Control (SMC), Backstepping Sliding Mode Control (BSMC) and the proposed ABSMC method under the same experimental conditions. The results demonstrate that the proposed ABSMC algorithm exhibits superior control performance compared to the SMC and BSMC method, with faster response speed and stronger robustness. Additionally, this method effectively mitigates the chattering issue.