Path-tracking and trajectory-tracking for a quadrotor are basic tasks when solving the motion control. The difference between path-tracking and trajectory-tracking is that the reference trajectory is generated by a suitable virtual quadrotor whereas the reference path is not required to be generated by a virtual quadrotor. In this paper, we propose a trajectory-tracking controller for an underactuated quadrotor. A new change in describing the dynamics of the quadrotor is presented from which we can determine the direction of motion of the quadrotor in the horizontal plane through its gravity center. After this change, we can separate the dynamics of the system into three sub-groups then combine with a coordinate transformation to design control for the quadrotor. The controller synthesis is based on Lyapunov direct method and the backstepping technique. Simulations illustrate the effectiveness of the proposed controller.