In wireless networks, it is very important to optimize the number of channels, due to the limit on the number of usable channels in a given network. In addition, multimedia services with high QoS requirements with respect to throughput and delay have recently become popular. To satisfy these requirements, it has become important to find a way of providing multipath transmission. A channel assignment algorithm is presented that minimizes the number of required channels while satisfying the throughput requirements of source-destination pairs in multichannel, multiradio, multirate wireless mesh networks. A mathematical model is proposed that considers interference effect, link capacity, and throughput requirements. A novel channel assignment algorithm is developed that takes into account multipath selection, channel reusability, link capacity sharing, and global optimization. The performance of the algorithm is compared with that of CPLEX, using 24 network scenarios. The maximum gap between the CPLEX solutions and those of the proposed algorithm is, on average, only 4.8%.