We introduce an original Model Predictive Control (MPC) approach, aimed at optimizing the energy production of an Inertial Sea Wave Energy Converter (ISWEC). The aim of the proposed method is to handle the performance tradeoff among different control objectives such as energy production, control effort and speed limitation through a suitable MPC formulation. Mechanical and electrical physical constraints are taken into account to ensure proper working conditions to the ISWEC system. We employ a linear model of the ISWEC device to cast the underlying MPC optimization problem as a quadratic program, to allow a fast online implementation of the controller by means of an efficient solver. We introduce extensive simulation tests performed on a detailed nonlinear ISWEC model to show the effectiveness of the presented approach.