The existing mathematical model of underwater vehicles is difficult to match the actual model with new emerging of underwater vehicles. In order to deal with modeling problem and predict space motion for new underwater vehicles, a black-box modeling method based on particle swarm optimization (PSO) and support vector machine (SVM) was proposed. Nonlinear mapping relationship between state of motion and thrusters for underwater vehicles was constructed by SVM. Optimal parameters of SVM were obtained through PSO algorithm. Then, a black-box model was established for underwater vehicles. Finally, by judging whether thrusters vary with time, space motion of a new kind of quadrotor underwater vehicle was adopted to verify the effectiveness of the proposed method. Space motion prediction results were evaluated by the root mean square error. The experimental results demonstrated that root mean square errors of the space motion prediction results were small. Space motion prediction results were in accordance with the actual space motion. The black-box model constructed by PSO and SUM was basically identical with the actual model and could effectively predict the space motion of underwater vehicles.