We investigate the feasibility of model predictive control (MPC) in ocean current turbine (OCT) control. A prediction model is obtained from a nonlinear model of a moored OCT via linearization. Three control inputs are assumed, the electromechanical torque applied to the rotor shaft and two blade pitch cyclic controls. The control problem contains is highly constrained, which prompts consideration of MPC. For MPC evaluation, comparisons with another constrained control technique, output variance constrained control, are included, as well as simulations of the linear and nonlinear OCT dynamics when the MPC strategy is applied.