The trajectory-tracking control problem is inves-tigated for an autonomous underwater vehicle (AUV) moving in the vertical plane using an internal point mass and a rear thruster as actuators. Combined with the dynamics of the point mass, the AUV is modeled as an underactuated system. A Lyapunov-based tracking controller is proposed by using back-stepping approach to stabilize the error dynamics and forcc the position errors to a small neighborhood of thc origin. Simulation results validate the proposcd tracking approach.