Wireless Mesh Network (WMN) is a promising model with benefits in coverage extension and throughput improvement. In WMN, multiple channels are available for improving system performance through concurrent transmission. For maximum utilization, per-node channel quality and inter-channel interference should be considered in multi-channel assignment. We propose a new multi-channel assignment method. First, we model the mesh network connectivity after a multi-graph which has multiple edges between two nodes. From this connectivity graph, we generate a multi-channel conflict graph, then we allocate multiple channels so that they do not overlap, using list coloring algorithm. We also propose a new sub-graph list coloring algorithm to enhance channel allocation performance. From computer simulations, we verify the performance of the algorithm.