This study involved channel modeling and characteristics analysis of unmanned aerial vehicles (UAVs) according to different operating trajectories. Based on the idea of standardized channel modeling, air-to-ground (AG) channel modeling of a UAV was carried out, taking into consideration that both the receiver (Rx) and the transmitter (Tx) ran along different types of trajectories. In addition, based on Markov chains and a smooth-turn (ST) mobility model, the influences of different operation trajectories on typical channel characteristics—including time-variant power delay profile (PDP), stationary interval, temporal autocorrelation function (ACF), root mean square (RMS) delay spread (DS), and spatial cross-correlation function (CCF)—were studied. The multi-mobility multi-trajectory UAV channel model matched well with actual operation scenarios, and the characteristics of the UAV AG channel could be analyzed more accurately, thus providing a reference for future system design and sensor network deployment of sixth-generation (6G) UAV-assisted emergency communications.