Circular synthetic aperture sonar obtains all-round observation information of underwater targets by performing 360° circular motion on the imaging scene to achieve high-precision three-dimensional imaging of underwater targets, whose imaging performance is significantly affected by the circular motion error of unmanned platforms. To address this issue, a centripetal acceleration based nonlinear guidance for circular (CANGC) was designed based on the derivation of the circular path, which has a high degree of fit to the circular trajectory and high control accuracy. In addition, a circular motion control law based on model predictive control (MPC) algorithm was designed, which has a fast control response and a strong adaptive ability. The two algorithms were well integrated to achieve accurate circular trajectory tracking, in which the control output of the guidance law is yaw rate, so that the control process does not rely on the yaw angle data measured by the magnetometer of the unmanned surface vehicle (USV) and can be used under conditions with strong magnetic field influence. The superiority of the algorithm was verified through simulation experiments, and the tracking accuracy of the algorithm proposed in this paper is 80.1% higher than that of the algorithm described in previous reference literature. Further validation was conducted through lake experiments, which shows high control accuracy for circular motion. The research results provide an algorithmic foundation for the development of unmanned ships used for circular synthetic aperture sonar imaging.