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This paper discusses the path planning and path following control problems of robotic fish. In order to avoid obstacles when robotic fish swim in a complex environment, a path planning method based on beetle swarm optimization (BSO) algorithm is developed. This method considers the influence of the robotic fish's volume and motion constraints on the path planning task, which can eliminate the collision risk and meet the constraint of the minimum turning radius when the robotic fish obtains the planned path. In constructing the path following controller, a multilayer perception based model predictive control (MPC) is adopted to design the optimal control method, and the objective function of the optimal control is dynamically adjusted according to the path curvature. The simulation results show that this proposed method can effectively overcome the complexity of robotic fish kinematics modelling and adapt well to the reference paths of different curvatures given by the path planner.