To facilitate the commercialization of wave energy in an array or farm environment, effective control strategies for improving energy extraction efficiency of the system are important. In this paper, we develop and apply model-predictive control (MPC) to a heaving point-absorber array, where the optimization problem is cast into a convex quadratic programming (QP) formulation, which can be efficiently solved by a standard QP solver. We introduced a term for penalizing large slew rates in the cost function to ensure the convexity of this function. Constraints on both range of the states and the input capacity can be accommodated. The convex formulation reduces the computational hurdles imposed on conventional nonlinear MPC. For illustration of the control principles, a point-absorber approximation is adopted to simplify the representation of the hydrodynamic coefficients among the array by exploiting the small devices to wavelength assumption. The energy-capturing capabilities of a two-cylinder array in regular and irregular waves are investigated. The performance of the MPC for this two-WEC array is compared to that for a single WEC, and the behavior of the individual devices in head or beam wave configuration is explained. Also shown is the reactive power required by the power takeoff system to achieve the performance.