To solve the trajectory tracking problem for the under actuated, strong coupled nonlinear system of the quadrotor aircraft, a sliding mode control strategy was proposed. Based on the typical Newton-Euler dynamics model, the UAV control system was divided into two subsystems: a fully actuated subsystem (ψ, z) and a under actuated subsystem(x, y, φ, θ). The variables ψ and z of the fully actuated subsystem converged to the desired value by using the terminal sliding mode controllers. Then, the second mode control was used to achieve effective position and attitude tracking of x, y, φ and θ, whose sliding mode surface parameters were obtained by using the Hurwitz theory. Simulation was made on Matlab/Simulink, and the results show that the designed trajectory controllers have high robustness and good performance for position and angle tracking.