This paper presents the optimal position of an aerial base station (ABS) by unmanned aerial vehicle (UAV) in a heterogeneous cellular network (HetNet) at heterogeneous user traffic demands to maximize the throughput. The key idea is to consider the upper limit of the achievable throughput based on the traffic demand of each user to optimize the ABS position, optimally selecting its direct communication path to the terrestrial base station or its forwarding path via the ABS. We derive the throughput maximization problem with traffic demands and then solve this problem for the ABS position with the optimal communication paths. Our simulation results highlighted that the proposed method achieved 23% higher throughput than an existing method at heterogeneous user traffic demands.