Hybrid access point (HAP) is a node in wireless powered communication networks (WPCN) that can distribute energy to each wireless device and also can receive information from these devices. Recently, mobile HAPs have emerged for efficient network use, and the throughput of the network depends on their location. There are two kinds of metrics for throughput, that is, sum throughput and common throughput; each is the sum and minimum value of throughput between a HAP and each wireless device, respectively. Likewise, two types of throughput maximization problems can be considered, sum throughput maximization and common throughput maximization. In this paper, we focus on the latter to propose a deep learning-based methodology for common throughput maximization by optimally placing a mobile HAP for WPCN. Our study implies that deep learning can be applied to optimize a complex function of common throughput maximization, which is a convex function or a combination of a few convex functions. The experimental results show that our approach provides better performance than mathematical methods for smaller maps.