In this paper, we investigate the air-to-ground multi-traffic backhaul enabled by unmanned aerial vehicle (UAV) equipped with multiple radio access networks (RANs). Faced with the challenging traffic designation problem over diverse RANs, an efficient packet delivery scheme based on multi-priority batch arrival queuing theory is proposed to match various traffics with multiple RANs. Specifically, our contributions are threefold: 1) The average queuing time of UAV-enabled multi-RAN access is theoretically derived according to multi-priority batch arrival queuing theory. 2) The priority factor and z-type utility function are well tailored by leveraging the derived queuing time. 3) A multiple traffic backhaul strategy is further proposed by exploiting the priority factor and z-type utility function to optimize the packet delivery, i.e., maximizing the delay utility via joint network selection and power allocation for diverse RANs. The simulation results show that the average delay of delay-sensitive packets is reduced by 15%, and the overall packet delivery quality is improved considerably. INDEX TERMS Unmanned aerial vehicle (UAV), resource allocation, queuing theory, multi-priority, traffic backhaul.