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Admission control plays a very important role in guaranteeing the quality-of-service (QoS) in wireless mesh networks (WMNs). In this paper, based on the channel and hidden terminal information, we first estimate the available bandwidth in the operation of medium access control (MAC). We then design an admission control algorithm (ACA) at the MAC layer to address the QoS issue for real-time and nonreal-time traffic. For real-time traffic, all nodes on a route make an admission control decision based on the estimated available bandwidth. For the nonreal-time traffic, a rate adaptation algorithm is proposed to adjust the sending rates of sources to prevent the network from entering the congestion state. Finally, through extensive simulations, we demonstrate the effectiveness of our algorithm.