Various control strategies for power regulation in variable-speed wind turbines commonly assume that the whole system parameters are known and available, which is not necessarily satisfied in practice. In this work, an adaptive control strategy, which neither need to know completely the system parameters nor the rotor acceleration, is proposed for power regulation and tracking. It also includes a (borrowed) pitch controller to increase the system performance. The strategy is formally proven by the Lyapunov method. The performance of the proposed controller is illustrated with the use of the wind turbine simulator FAST code.