Providing end-to-end delay bound for real-time applications is a major challenge in wireless mesh networks (WMNs) because the bandwidth requirements of flows are time-varied and the channel condition is unstable due to the wireless interference between the links. In this paper, we present a two-stage slot allocation mechanism in TDMA-based WMNs. First, we assume that the bandwidth requirement of each flow is given in the form of a range and use a distributed algorithm to pre-allocate time slots to each link. Then, we implement an On-The-Go scheduling scheme, which enables each link to schedule its transmission time promptly without coordinating with others. In contrast to traditional approaches, our method allows a degree of control over the collision probability, but it only requires a few control messages and the computational overhead is lower. The simulation results show that our mechanism performs efficiently and flexibly on supporting real-time applications in WMNs.