In this paper, an algorithm based on the multi-player multi-armed bandit (MAB) framework is proposed to solve an uncoordinated spectrum access problem. The proposed technique does not require any communication or coordination between users. The case of varying channel rewards across users is considered. In contrast to previous work, the users are permitted to choose multiple channels for transmission, resulting in a MAB model with multiple plays. The proposed algorithm has an expected regret of the order O(log 2 T), which is validated by simulation results. Index Terms-uncoordinated spectrum access, multi-armed bandits with multiple plays, varying reward distribution.