Multiuser access is a critical issue in distributed cognitive radio networks (DCRNs), as the collisions among the competing secondary users (SUs) may decrease the network throughput significantly. In order to reduce the collisions, we propose a dynamic backoff algorithm to find an optimal backoff contention window to maximize the network throughput and reduce the channel access delay. Based on the proposed algorithm, a multichannel medium access control (MAC) protocol with dynamic backoff contention (MMAC-DB) is designed. In this protocol, the time duration of each channel is divided into four phases: idle, sensing-sharing, contention, and data transmission. The dynamic backoff algorithm is implemented in the contention phase. Moreover, a duration tradeoff is made between the data transmission phase and the contention phase. The effectiveness of the proposed protocol is examined by extensive simulations, which shows that the proposed protocol can enhance the throughput and reduce the channel access delay.