Unmanned Surface Vehicle (USV) is a novel multifunctional platform for ocean observation, and its heading and velocity control are essential and important for autonomous operation. A coupled heading and velocity controller is designed using backstepping technology for an USV called `USBV` (Unmanned Surface Bathymetry Vehicle). The USBV is an underactuated catamaran, where the heading and velocity are controlled together by two thrusters at the stern. The three degrees-of-freedom equations are used for USBV`s modeling, which is identified using experiment data. The identified model, with two inputs, induces heading and velocity tracking, which are coupled. Based on the model, a nonlinear controller for heading and velocity are acquired using backstepping technology. The stability of the controller is proved by Lyapunov theory under some assumptions. The verification is presented by lake and sea experiments.