We propose a reinforcement learning approach with function approximation for maximizing the power output of wind turbines (WTs). The optimal control of wind turbines majorly uses the maximum power point tracking (MPPT) strategy for sequential decision-making that can be modeled as a Markov decision process (MDP). In the literature, the continuous control variables are typically discretized to cope with the curse of dimensionality in traditional dynamic programming methods. To provide a more accurate prediction, we formulate the problem into an MDP with continuous state and action spaces by utilizing the function approximation in reinforcement learning. The commonly used pitch angle is selected as a control variable we are concerned with, which is regarded as the system state along with some other controllable and uncontrollable variables proven to affect the power output. Computational studies of real data are conducted to demonstrate that the proposed method outperforms the existing methods in the literature in obtaining the optimal power output.