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With the increase in Electric Vehicles (EVs) penetration, their charging needs form an additional burden on the grid. Thus, charging coordination is necessary for safe and efficient EV use. The scheduling of EVs is especially essential in Vehicle-to-Grid schemes, where EVs energy cost can be reduced by intelligently managing the charging and discharging according to real-time prices and owners' needs. Further, utilities can perform load shifting by price-based demand-response programs. However, the scheduling problem is challenging in the presence of multiple unknown variables, such as real-time prices, commuting behavior, and energy needs. Most of the scheduling techniques attempt to model the system uncertainties (e.g., forecast prices) and plan accordingly. In this paper, we propose the use of a model-free Reinforcement Learning (RL) technique that can deduce a charging/discharging strategy without requiring any model of the system. We evaluate the performance of the proposed system with real-world data and investigate the learned charging/discharging pattern to show the effectiveness of the proposed method.