Recently, much attention has been paid to the problem of how to efficiently utilize multiple orthogonal channels and communication radios to enhance the aggregate throughput of a Wireless Mesh Network (WMN). Most of prior works on the channel assignment problem assume that all transmission links can only transmit at the base rate and do not consider the presence of multiple bit-rates. However, in a multi-rate environment, the achievable throughput of a high-rate link is critically affected by neighboring low-rate links when they share the same channel. This problem is called performance anomaly . To cope with the problem, we propose a Rate-Loss function, which is a quantitative metric used to evaluate how critical the performance anomaly problem occurred in each orthogonal channel. In addition, we present a distributed Rate-Loss based Channel Assignment (RL-CA), which enables each router to select channels suffering from the slightest performance anomaly problem in a distributed manner. The simulation results show that RL-CA outperforms existing schemes and can adapt to network dynamics efficiently.