We propose a distributed MAC protocol for cognitive radio when primary network is IEEE 802.16e/m WiMAX. Our proposed MAC protocol is Truncated Binary Exponential Backoff Algorithm where backoff stage of algorithm is doubled at each collision, and backoff counter is operated by frame basis and is freezed at a frame with no idle slots. We model our proposed MAC protocol as a 3-dimensional discrete-time Markov chain and obtain steady state probability of the Markov chain by using a censored Markov chain method. Based on this steady state probability, we obtain the throughput, packet loss probability and packet delay distribution of secondary users. Our numerical examples show that initial contention window size can be determined according to the number of secondary users in order to obtain higher throughput for secondary users, and the maximum backoff stage has a large impact on the secondary user’s packet loss probability.