Sea wave energy converter control is a non-causal optimal control problem, and the control performance relies on the accuracy of wave prediction information. However, the existing wave prediction methods, such as Auto-Regressive (AR) method, extended Kalman Filter (EKF), Artificial neural network and deterministic sea wave prediction (DSWP), inevitably introduce prediction errors. This paper presents a robust non-causal linear optimal control of wave energy converters to explicitly cope with the prediction error of sea wave prediction and simultaneously compensate the modelling uncertainty caused by wave force approximations. This is achieved by designing a non-causal linear optimal control (LOC) to maximize the energy output and a sliding mode control (SMC) to compensate unmodeled WEC dynamics and wave prediction error. The parameters of both SMC and non-causal LOC are calculated off-line, which significantly enhances the real-time implementation of the proposed controller with reasonably low computational load. Simulation results demonstrate the efficacy of the proposed control strategy.