In this paper, we propose a novel path tracking control algorithm for an underactuated autonomous underwater vehicle (AUV). The underactuated AUV is controlled by the thrust force and the yaw torque: no sway thruster is used. To deal with this underactuated AUV problem in the path tracking, we introduce an approach angle which makes the AUV converge to the reference path. To design the path tracking controller, we obtain the vehicle's error dynamics in the body-fixed frame, and then design the path tracking controller based on the dynamic surface control (DSC) method. The proposed controller only needs the information of the position and the heading angle of the reference path. Some simulation results demonstrate the effectiveness of the proposed controller.