In multi-hop cognitive radio networks (CRNs), there can be dramatic increase in end-to-end delay when a traffic flow switches between a number of channels along its path. We propose a new Maximum Flow-Segment (MFS) based scheme to channel assignment in CRN by minimizing the number of times the channel is switched along a flow. Our MFS based scheme has been efficiently integrated into the AODV on-demand routing protocol. We demonstrate that our MFS based scheme reduces the number of channel switches for the traffic flows and reduces the end-to-end delay by 50%. Our scheme also minimizes the routing overhead, and achieves a higher and more stable throughput than the link based approach.