To improve the quality of service (QoS) on the internet of medical things, a cognitive radio (CR) protocol based on orthogonal frequency division multiple access (OFDMA) is proposed, named CR-OFDMA. In this protocol, we divide a complete channel into multiple orthogonal subchannels and enhance the subchannel assignment scheme, which achieves QoS improvement under consideration of priority and fairness. Furthermore, we improve spectrum resource utilization by fully utilizing the remaining subchannels, feedback slots, and backoff slots. Then, a two-dimensional Markov model is established to describe the dynamic characteristics of the protocol operation, where the backoff stage and the backoff counter value constitute the system state. By establishing the traffic conservation equations for the system operation, the transmission probability and collision probability are calculated, and expressions of system throughput, channel utilization, and fairness index are derived. Finally, numerical results validate the advantages of CR-OFDMA.