In order to meet the needs of marine exploration and underwater reconnaissance, a bionic jellyfish robot with multiple degrees of freedom is designed. The Robotic Toolbox in Matlab analysis software is used to establish the model of the jellyfish manipulator, performing the motion simulation. After analyzing the kinematics and dynamics, the curves of angular velocity and angular acceleration are obtained. Based on the torque curve of reverse launch, the 3-D model imported into Adams is driven and simulated, and a simple BP neural network control algorithm is constructed by using the Jtraj function to carry out 5-time polynomial trajectory planning for the robotic arm of the bionic jellyfish robot with four degrees of freedom. The simulation results show that the motion curves are continuous and smooth without mutation, and can meet the actual demand.