This work studies unmanned aerial vehicle (UAV) relay-assisted Internet of Things (IoT) communication networks in which a UAV is deployed as an aerial base station (BS) to collect time-constrained data from IoT devices and transfer information to a ground gateway (GW). In this context, we jointly optimize the allocated bandwidth, transmission power, as well as the UAV trajectory to maximize the total system throughput while satisfying the user's latency requirement and the UAV's limited storage capacity. The formulated problem is strongly non-convex which is very challenging to solve optimally. Towards an appealing solution, we first introduce new variables to convert the original problem into a computationally tractable form, and then develop an iterative algorithm for its solution by leveraging the inner approximation method. Numerical results are given to show significant performance improvement over benchmark schemes.