The main purpose of this paper is to present a novel algorithmic reinforcement learning (RL) method for damping the voltage and frequency oscillations in a micro-grid (MG) with penetration of wind turbine generators (WTG). First, the continuous-time environment of the system is discretized to a definite number of states to form the Markov decision process (MDP). To solve the modeled discrete RL-based problem, Q-learning method, which is a model-free and simple iterative solution mechanism is used. Therefore, the presented control strategy is adaptive and it is suitable for the realistic power systems with high nonlinearities. The proposed adaptive RL controller has a supervisory nature that can improve the performance of any kind of controllers by adding an offset signal to the output control signal of them. Here, a part of Denmark distribution system is considered and the dynamic performance of the suggested control mechanism is evaluated and compared with fuzzy-proportional integral derivative (PID) and classical PID controllers. Simulations are carried out in two realistic and challenging scenarios considering system parameters changing. Results indicate that the proposed control strategy has an excellent dynamic response compared to fuzzy-PID and traditional PID controllers for damping the voltage and frequency oscillations.