Unmanned surface vessels (USVs) have been widely utilized in marine transportation and hold significant strategic importance in economic development. USVs require efficient and precise control algorithms to achieve effective trajectory tracking and obstacle avoidance. Model predictive control (MPC) is a widely used trajectory tracking algorithm for USVs. The accuracy of MPC relies mainly on high-precision dynamic mechanism models. However, existing mechanism models often fail to obtain accurate hydrodynamic parameters, and their model structures may not be suitable, reducing the performance of MPC. To improve the performance of MPC for USV trajectory tracking and obstacle avoidance, a data-driven nonlinear model predictive control (DNMPC) algorithm based on nu support vector regression (nuSVR) is proposed in this paper. DNMPC uses nuSVR to establish a data-driven dynamic model for the USV. Then, DNMPC formulates the trajectory tracking problem as a single-objective optimization problem with input constraints. Additionally, an output constraint is introduced to achieve obstacle avoidance. An Ivy intelligent optimization algorithm is also employed to solve this multiconstraint optimization problem. To validate the effectiveness of the proposed algorithm, a CyberShip II USV is used for tracking multiple trajectories and obstacle avoidance. The experimental results demonstrate that the DNMPC approach achieves precise trajectory tracking and obstacle avoidance.