This paper presents the application of nonlinear model predictive control (NMPC) to a point absorber wave energy converter (WEC). Model predictive control (MPC) is generally a promising approach for WECs, since system constraints and actuator limits can be taken into account. Moreover, it provides a framework for defining optimal energy capture and it can benefit from predictions. Due to possible nonlinear effects, such as the mooring forces, an NMPC is proposed in this paper, whose performance is compared to that of a linear MPC. Both controllers are supposed to control a nonlinear point absorber model. Computer simulations show that the proposed NMPC is able to optimize the energy capture while satisfying system limits.