Autonomous docking and undocking control is an important part of intelligent ship motion control. In this study, the adaptive-mutation beetle swarm prediction (AMBS-P) algorithm is used to propose a control approach for autonomous docking and undocking. Firstly, this paper introduces the principle of the AMBS-P algorithm, then the convergence is proved. Secondly, the “Tito-Neri” model ship is introduced as a case study, and the thrust allocation process is described. Finally, the effect of docking and undocking is verified in multiple scenarios starting from different angles. In the verification, first of all, when designing the docking and undocking controllers, the correctness of the algorithm and the practicality of the control are verified by whether there is ship drag or not. Secondly, by analyzing the parameters of the algorithm, the optimal parameters of it are determined and verified in the real environment. Thirdly, compared with typical proportion–integral–derivative (PID) algorithm and nonlinear model predictive control (NMPC) algorithm, the AMBS-P algorithm has better results for autonomous docking and undocking control, no matter in long-distance or short-distance. The research shows that the AMBS-P algorithm has a fast response and good effect for the ship autonomous docking and undocking, and does not rely too much on the system model.