Wireless powered communication technology has a great potential to power low-power wireless sensor networks and Internet of Things (IoT) for real-time applications in future 5G networks, where age of information (AoI) plays a very important performance metric. This paper studies the system average AoI of a wireless powered network, where a wireless-powered user harvests energy from a wireless power source (WPS) and then transmits data packets to its access point (AP) by using the harvested energy. The user generates data packets with some probability and adopts the first-come-first-served (FCFS) service policy. For such a system, by using the queuing theory and the probability models, we derive a closed-form expression of the system average AoI. We also formulate an optimization problem to minimize the AoI by optimizing the data packet generating probability, and find its solution by simple calculation and search. Simulation results demonstrate the correctness of our obtained analytical results. It also shows that, when the total distance of the two hops is fixed, the system average AoI increases linearly with the increment of the distance of the first hop, and a smaller data packet generating probability should be selected to match a bigger first-hop distance for achieving a smaller system average AoI. Moreover, a smaller data packet size also contributes to a smaller system average AoI.