This paper considers an unmanned aerial vehicles (UAV) communication network, where UAV operate as an aerial mobile relay between a source and a destination of the network. To capture the “timeliness” of the received information at the destination node, a new performance metric named age of information (AoI) is considered. In addition, a short packet communication scheme maintains low latency in the proposed UAV wireless communication system. The finite block-length theory investigates the performances of short packet communications scheme in the UAV-assisted wireless communications system. In this paper, the Average Age of Information (AAoI) is estimated by applying the Stochastic Hybrid Systems (SHS) model. The SHS model comprises discrete states represents events that reset the AoI process and continuously dynamics that represent linearly growing age processes. Finally, a closed-form expression for the AAoI of the proposed UAV wireless communication system is derived and it can be used to estimate the optimal altitude, block length and other parameters.