IEEE802.11s draft proposes a new medium access control function-mesh deterministic access (MDA), which is mainly used for single-channel wireless mesh local area network (LAN). In single-channel environment, collisions between control packets and data packets may occur very often. To completely avoid the collision between control packets and data packets, the mesh delivery traffic indication message (DTIM) interval is first divided into contention period and data transmission period. To reduce the hardware requirements in design, we require a mesh point (MP) only equips a single transceiver to support multichannel environment. To provide higher performance and network capacity than the original MDA for wireless mesh LAN, we proposed a multichannel MDA (MMDA) algorithm. However, the MMDA algorithm may suffer from the resource waste problem when wireless mesh LAN is at heavy-loading situation, so this paper proposes a dynamic adjustable contention period (DACP) mechanism to solve this problem. In addition, we use an adaptive backoff process (ABP) to improve the fairness of the MMDA algorithm. The theoretical analysis gives the upper limit of the throughput for the DACP mechanism. The simulation experiments clearly show the results in multichannel wireless mesh LAN environment that the proposed scheme performs better than the MMDA algorithm and the enhanced distributed channel access (EDCA) in throughput, average waiting time, and packet drop ratio.