A stochastic model was applied to devise an optimal algorithm for the rotational speed control of an oscillating-water-column (OWC) wave power plant equipped with a Wells turbine and to evaluate the average power output of the plant. The hydrodynamic coefficients for the OWC are assumed known (as functions of frequency), as well as the turbine performance curves. The whole model is based on linear control theory of a stochastic process, it being assumed that the sea surface elevation has a Gaussian probability density function. The optimal control law is expressed in terms of a simple relationship between the instantaneous values of the electromagnetic torque (to be applied on the generator rotor) and the rotational speed. It is remarkable that the optimal control algorithm was found to be practically insensitive to wave climate. A simple additional algorithm, accounting for constraints imposed by the electrical grid on power oscillations, was derived in order to complement the optimal control law.