This paper proposes an efficient computation task offloading mechanism for mobile edge computing (MEC) systems. The studied MEC system consists of multiple user equipment (UEs) and multiple radio interfaces. In order to maximize the number of UEs benefitting from the MEC, the task offloading and power control strategy for a UE is optimized in a joint manner. However, the problem of finding the optimal solution is NP-hard. We then reformulate the problem as a Markov decision process (MDP) and develop a reinforcement learning- (RL-) based algorithm to solve the MDP. Simulation results show that the proposed RL-based algorithm achieves a near-optimal performance compared to the exhaustive search algorithm, and it also outperforms the received signal strength- (RSS-) based method no matter from the standpoint of the system (as it leads to a larger number of beneficial UEs) or an individual (as it generates a lower computation overhead for a UE).