The application of multi-hop wireless Ad Hoc networks (WANETs) has been facing a great challenge to implement cooperative control over user transmission rates under the resource restrictions. In this paper, we propose an efficient bandwidth allocation scheme called Active-Time based Bandwidth Allocation Scheme (ATBAS) that can ensure fair bandwidth allocation among the users in a multi-hop WANET model. This scheme operates at each hop and fairly allots each competing flow a share of channel time, according to which each hop then computes the updating rate for each flow traversing the hop and records their updated rates into each data packet's special control header. The source of each flow in this scheme can eventually adjust its sending rate to reach its fair share. An algorithm is developed to implement the above mechanism. We will show through simulation results that our proposed algorithm is able to fairly distribute bandwidth among multi-hop flows.