In this paper, we propose an efficient quality-of-service routing protocol in cognitive radio mobile ad hoc networks (CR-MANETs), where a QoS route is formed by exploiting deep reinforcement learning (DRL) and cross-layer design technology to avoid the affected region of a primary user. In the forwarding route request (RREQ) process, based on the designed DRL model, the proposed QoS routing protocol unicasts a RREQ packet to its neighbor with a minimum Q*-value satisfying energy and cognitive radio constraints. The Q*-value for each link is obtained by optimizing joint residual energy and speed of all nodes belonging to this link. Simulation results show that the proposed QoS routing protocol outperforms the CR-ad hoc on-demand distance vector routing one in terms of control overhead, packet delivery ratio, routing delay, and energy consumption, arising as an intelligent routing protocol in CR-MANETs.