As a non-causal optimal control problem, the performance of wave energy converter (WEC) control relies on the accuracy of the future incoming wave prediction. However, the inevitable prediction errors can degrade WEC performance dramatically especially when a long prediction horizon is needed by a WEC non-causal optimal controller. This paper proposes a novel non-causal linear optimal control with adaptive sliding mode observer (NLOC+ASMO) scheme, which can effectively mitigate the control performance degradation caused by wave prediction errors. This advantage is achieved by embedding the following enabling techniques into the scheme: (i) an adaptive sliding mode observer (ASMO) to estimate current excitation force in real-time with explicitly formulated boundary of estimation error, (ii) an auto-regressive (AR) model to predict the incoming excitation force with explicitly formulated boundary of prediction error using a set of latest historical data of ASMO estimations from (i), and (iii) a compensator to compensate for both the estimation error and the prediction error of excitation force. Moreover, the proposed NLOC+ASMO scheme does not cause heavy computational load enabling its real-time implementation on standard computational hardware, which is especially critical for the control of WECs with complicated dynamics. The proposed NLOC+ASMO framework is generic and can be applied to a wide range of WECs, and in this paper we demonstrate the efficacy by using a multi-float and multi-motion WEC called M4 as a case study, whose control problem is more challenging than the widely studied point absorbers. Simulation results show the effectiveness of the proposed control scheme in a wide range of sea states, and it is also found that the controller is not sensitive to change of ASMO parameters.