This paper investigates the problem of spectrum assignment and sharing to minimize the total delay of multiple concurrent flows in multi-hop cognitive radio networks. We first analyze the expected per-hop delay, which incorporates the sensing delay and transmission delay characterizing the PU activities and spectrum capacities. Then we formulate a minimum delay optimization problem with interference constraints, and propose an approximation algorithm termed MCC to solve the problem. According to our theoretical analysis, MCC has a bounded performance ratio and a low computational complexity. Finally, we exploit the minimum potential delay fairness in spectrum sharing to mitigate the inter-flow contentions. Extensive simulation study has been performed to validate our design and to compare the performance of our algorithms with that of the state-of-the-art.