A direct drive wave power generation system (DDWPGS) has the advantages of a simple structure and easy deployment, and is the first choice to provide electricity for islands and operation platforms in the deep sea. However, due to the off-grid, the source and load cannot be matched, so accommodation is an important issue. Hydrogen storage is the optimal choice for offshore wave energy accommodation. Therefore, aiming at the source-load mismatch problem of the DDWPGS, an electric-hydrogen hybrid energy storage system (HESS) for the DDWPGS is designed in this paper. Based on the characteristics of the devices in the electric-hydrogen HESS, a new dynamic power allocation strategy and its control strategy are proposed. Firstly, empirical mode decomposition (EMD) is utilized to allocate the power fluctuations that need to be stabilized. Secondly, with the state of charge (SOC) of the battery and the operating characteristics of the alkaline electrolyzer being considered, the power assignments of the battery and the electrolyzer are determined using the rule-based method. In addition, model predictive control (MPC) with good tracking performance is used to adjust the output power of the battery and electrolyzer. Finally, the supercapacitor (SC) is controlled to maintain the DC bus voltage while also balancing the system’s power. A simulation was established to verify the feasibility of the designed system. The results show that the electric-hydrogen HESS can stabilize the power fluctuations dynamically when the DDWPGS captures instantaneous power. Moreover, its control strategy can not only reduce the start-stop times of the alkaline electrolyzer but also help the energy storage devices to maintain a good state and extend the service life.