This paper proposes a MIMO linear quadratic regulator (LQR) controller designed for a horizontal variable speed wind turbine with focus on the operating range referring to the above rated wind speeds. The operating conditions of wind turbines make them subject to fluctuating loads that create fatigue and lead to damage. Alleviating these loads would reduce the needed materials, and increase the lifespan and the quality of the produced energy. The optimality of the entire system is defined in relation with the trade-off between the wind energy conversion maximization and the minimization of the fatigue in the mechanical structure. The solution of a control using an LQR regulator is presented. The performances of the optimal control are assessed and discussed by means of a set of simulations.