The Wireless Mesh Network (WMN) has been an emerging technology in recent years. Because the transmission medium used in networking Mesh APs is radio, WMN is not only easy and cost effective in deployment, but also has good scalability in coverage area and capacity. The IEEE 802.11 MAC protocol has been adopted as the de-facto medium access control. We assess the fitness of the IEEE 802.11 over WMN, and contend that it is really necessary to be changed so that it can be adapted to WMN. In this paper, we propose the MASH (Medium Access with ScHeduling) protocol, which schedules the packet transmission between Mesh APs in a fully-distributed manner. Since out-of-band signaling is used and scheduling is executed to solve the hidden terminal problem and exposed terminal problem, the simulations show that both the network throughput and end-to-end delay can be significantly improved in this wireless multi-hop network.