Aiming at the problem of self-stabilizing flight and trajectory tracking control for quadrotor aircraft, a multi-modal sliding-mode attitude control and a new back-stepping recursive trajectory tracking control method are proposed. Firstly, the kinematics equation is established according to Newton's Second Law and Euler's Equation. Considering the serious coupling between the outer loop position tracking control and the inner attitude, the outer loop position controller adopts the new inverse method, which is simple, effective and easy for engineering application. To the inner loop attitude control, a switching type sliding mode control law is designed based on the multi-slide-mode design concept by combining the characteristics of linear sliding mode with nonsingular terminal sliding mode. This control law allows the system state to run in the optimal mode while ensuring that the system's arrival time and sliding time are limited, thus fast global convergence is realized. Simulation results show that the designed controller can quickly track the desired attitude and trajectory and has good control effect.