A cognitive radio ad hoc network (CRAHNs) is an infrastructure-free network containing a cognitive radio, which can use the spectrum resources effectively through an adaptive change of parameter settings and decision-making. Hence, it enhances the spectrum efficacy for satisfying the growing mobile traffic requests. In multihop CRAHNs, in order to ensure a reliable transmission and energy efficiency, the routing protocol should consider the metrics of channel quality, link stability, and energy consumption. In this paper, a Fuzzy-Markov routing policy and priority-based load balancing algorithm (FMRP-PLB) for CRAHNs is designed. In this protocol, a combined routing metric is derived using delay, energy rate, and link expiration time metrics. For modeling the channel state, a Fuzzy-Markov decision model is designed, in which the channel states and spectrum availabilities of SU are modeled as state transition matrices. Then, optimum routing decisions are made using the combined routing metric and the predicted transmission success probability. A load balancing metric (LBM) is derived in terms of available link capacity, remaining buffer size of node, and back-off delay. During data transmission, based on the traffic priority and measured levels of LBM, the optimum paths are selected. Simulation results using NS2 suggest that FMRP-PLB attains an increased packet delivery ratio with reduced delay and energy consumption.