Sea wave energy converter (WEC) control plays a vital role in maximizing energy output, and the control performance highly relies on the effective sensors which provide real-time measurements and determine the control action. This paper investigates a new WEC control problem, which is the energy maximization subject to sensor and actuator faults. Fault detection for wave energy converters is of great importance in maintaining the high reliability of the system. This paper presents a robust fault diagnosis approach effectively detecting sensor and actuator faults in real-time. A compensator is then designed to minimize the influence from faults and maintain the control performance. A non-causal linear optimal control is applied to maximize the energy output, in which the future excitation force is incorporated to determine the current control action. This approach can also be straightforwardly applied to other control methods. The parameters of the proposed fault detection method and fault-tolerant control method can be calculated off-line, which enhances the real-time implementation with a low computational burden. A realistic sea wave collected from the coast of Cornwall, UK is used to demonstrate the efficacy of the proposed approach.