Mobility can lead to continual loss of data and service interruptions during communications in multi-hop cognitive radio networks. Mobility of primary users (PUs) or cognitive users (CUs) requires adjustment of multi-hop communications among CUs to avoid any interference to PUs. To provide durable and reliable data routing that ensures continuous network service, we propose mobility-aware cognitive routing (MCR) for multi-hop cognitive radio networks. MCR examines the risk level of each node against interference regions and selects the most reliable path for data delivery using a Markov predictor. Through simulation, we verify that the proposed scheme can avoid route destruction preemptively and achieve reliable data delivery.