The application of unmanned surface vehicles in ocean surveying and mapping is more and more extensive, and course stability is an important basis for its autonomous navigation. An unmanned surveying and mapping catamaran for carrying measurement equipments and achieving mapping was designed in this paper. In order to realize course control of the unmanned vehicle, the RBF neural network was combined with the PID algorithm, and the self-learning ability of the RBF neural network can adjust the parameters of the PID controller autonomously. In the simulation process, the RBF-PID adaptive model, the single PID model and the BP-PID adaptive model which was introduced as the control group were simulated separately, and random disturbances were added at a same time to observe the system response. The results show that the course controller based on RBF-PID algorithm has zero overshoot and the shortest steady-state time. At the same time, it can correct the influence of random disturbances timely and effectively to ensure the heading stability of the unmanned surveying and mapping vehicle.