Due to the development of the 6th generation (6G) network, the integrated ground and air emergency communication system has an important impact on ensuring stable and efficient feedback links in major events and emergencies. Ground base stations (GBSs) and unmanned aerial vehicles (UAVs) and are key components of the air-ground network, providing access services for mobile Internet of Things (IoT) users. In this work, the cooperation between GBSs and UAVs is considered to achieve user matching problems in UAV-assisted air-ground networks, which can be described as a mixed integer nonlinear programming problem. Due to the difficulty of obtaining the best solution through exhaustive search in largescale networks, a GBS-oriented matching algorithm is proposed to handle the user association between the user, UAV and GBS. A restricted two-levels matching based approach with cyclic preferences (R-TMUA) is implemented to obtain stable solutions. In addition, to improve the efficiency of the algorithm model and reduce redundancy, this article proposes two bilateral matching algorithms, which consist of a user-UAV matching algorithm based on Gale-Shapley (GS) and a UAV-GBS matching algorithm based on random path to pair stable (RPPS). The simulation results demonstrate that the proposed algorithm outperforms traditional user matching schemes and has the capability to accommodate a greater number of users compared to conventional methods.