This paper explores an event-triggered model predictive control (MPC) approach for marine pumped hydroelectric storage (MPHS) to achieve the real time offshore wind-wave power complementarity in an integrated offshore renewable energies (OREs) and MPHS system. A deep learning wind-wave power predictor is proposed for ultra-short term power forecasting of the OREs based on feature extraction and fusion. Then, a real time nonlinear explicit MPC method is proposed based on an explicit model for controlling the MPHS such that the power oscillations from the OREs can be compensated timely. The stability of the real time MPC is proved and an event-triggered scheme is designed such that a good balance between the dynamic performance and regulation burden of the MPHs can be achieved. The proposed approach is demonstrated through a case study and the results indicate that the MPHS can be controlled to handle the OREs uncertainties timely and hence can meet the load demand with high accuracy (>97 %) by using the proposed control.