In order to carry out offshore operations smoothly in severe sea conditions, a shipborne Stewart platform for wave compensation is required. Due to the random characteristics of waves, traditional control algorithms cannot accurately compensate for the motion caused by a wave. For the electric shipborne Stewart platform, this paper proposes a backpropagation (BP)-neural-network-based proportional–integral–derivative (PID) control algorithm where the PID parameters are adaptively adjusted by a BP neural network. The control algorithm can improve the robustness and wave compensation precision of the wave compensation system. First, a numerical system model of the shipborne Stewart platform was established according to the classical kinematic model and dynamic model. Then, the BP-PID control algorithm was designed based on the joint space control. In order to reduce the network’s sensitivity to local details and quickly find the global minimum, the gradient descent method with the momentum term is used in the neural network. At last, the availability and rationality of the new method were substantiated through a simulation comparison under various sea conditions. The simulation results indicate that the proposed control method achieves a higher compensation accuracy in three directions under various sea states, compared with traditional PID control algorithm. Under the irregular wave disturbance, the new control method can reduce the position deviation by about 6.56 times compared with a traditional PID control algorithm. The new control algorithm will play an active role in the control of the shipborne Stewart platform.