Fault tolerance is critical to the real applications of underwater robots in complex underwater environments. In this paper, a biomimetic robotic fish with a stuck tail joint is used as the control object, and the fault-tolerant control method is proposed to control the faulty robotic fish to reach the specified speed. Specifically, based on the yaw fault-tolerant control, we firstly analyze the coupling problem between the control parameters of the robotic fish and design the feedback controller based on the central pattern generator model. In order to solve the problem that the feedback controller converges slowly, a multi-layer perceptron-based feedforward controller is proposed. Simulation experiments are designed to test the performance and effectiveness of the control system. Simulation results reveal that the proposed fault-tolerant control method is able to realize the speed control of faulty robotic fish while maintaining the yaw state stability.