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Considering that the traditional inner-outer loop control strategy of quadrotor helicopter depends on the time-scale separation assumption, the stability analysis is complex and the selection of control parameters is difficult, a trajectory tracking controller which is different from the traditional inner-outer loop control strategy is proposed. Firstly, the mathematical model of quadrotor helicopter is transformed to be three cascaded subsystems: altitude, yaw angle and vertical-horizontal subsystems. Then, terminal sliding mode control method is used to design the controller of altitude and yaw angle subsystems, so that the state errors of the two subsystems can converge to the origin in a finite time. Then, the vertical-horizontal subsystem is designed based on nonlinear variable transformation The stability of the closed-loop system is analyzed. It is proved that the designed trajectory tracking controller can ensure that the tracking error of the closed-loop system is asymptotically stable to the origin. Finally, the simulation results verify the effectiveness of the proposed controller.