This article investigates the problem of distributed channel selection in opportunistic spectrum access (OSA) system in which the channel states varying from slot to slot due to the influence of fading. The existing work considering with timevarying environment supposed users can receive a reward after successful contention of a channel. This assumption is not conformed to the realistic dynamic channel environment since the SNR at the receiver may be lower than a threshold value that the receiver can't receive information accurately. In this article, user can receive a positive reward only after a successful contention of a channel as well as the SNR at the receiver larger than the threshold value, otherwise, receive a zero reward. We formulate the channel selection problem as a non-cooperative game and prove it is a potential game which has at least one pure strategy Nash equilibrium. In addition, we propose a multi-agent learning algorithm. Users just need the current reward to learn to adj ust channel selection strategy.