The unmanned aerial vehicle (UAV), which is prominent in its flexibility and low cost, is considered to be fully utilized in the future wireless communication system to provide flexible services and improve connectivities. In this paper, we investigate the resource allocation problem in a wireless powered UAV communication system. In this considered system, The UAV acts as hybrid access point (HAP), which can first perform wireless power transfer in the downlink and charge the Internet of Thing (IoT) user devices (UDs). The UDs can use the harvested energy to deliver the data to the UAV. In the uplink, we explicitly consider short packet communication (SPC) as the transmission feature, which adopts finite block-length codewords and suffers from rate degradation. With the objective to maximize system energy efficiency, we jointly optimize the position and transmit power of the UAV, and transmission time of each UD. To address the formulated non-convex problem, we develop efficient algorithms to find sub-optimal solutions. Extensive simulations are conducted to verify the effectiveness of the proposed scheme.