This paper investigates the performance of an Internet of Things (IoT) system utilizing a unmanned aerial vehicle (UAV) in an urban environment with the assistance of non-orthogonal multiple access (NOMA) based mobile-edge computing (MEC). We consider two clusters of IoT device (ID) with limited resources that can harvest energy from a power beacon (PB) in order to offload their tasks to a UAV. We propose a four-phase protocol for energy harvesting (EH) and offloading task of IDs. To evaluate offloading performance, we derive the expression of successful computation probability (SCP) for the whole system. In addition, we present a formulation of the optimization problem that optimizes the SCP by optimizing the EH time and height of the UAV. The issue was resolved using particle swarm optimization (PSO). On the basis of the Monte Carlo simulation, a number of system parameters, including the number of IDs in each cluster, the EH time, and the height of the UAV, are evaluated to verify the accuracy of our analysis.