UAV-based base station (UBS) has played an important role in the air-ground integration network due to its high flexibility and nice air-ground wireless channels. Especially in Internet of Things (IoT) services, UBS can provide an efficient way for data collection from the IoT devices. However, due to the continuous mobility of UBS, the communication durations of devices in different locations with the UBS are not only time-limited, but also vary from each other. Therefore, it is a challenging task to analyze the throughput performance of the UAV-based IoT network. Accordingly, in this paper, we consider an air-ground network in which UAV flies straightly to collect information from the IoT devices based on CSMA/CA protocol. An analytical model analyzing the performance of this protocol in the network is proposed. In detail, we set up the system model for the network, and propose a new concept called quitting probability. Then, a modified Markov chain model integrating the quitting probability is introduced to describe the transmission state transition process and an accurately theoretical analysis of saturation throughput is given. In addition, the effects of the network parameters are discussed in the simulation section.