In this paper, we propose a method that estimates an average delay of frames for each queue and finds an optimal number of aggregated Medium Access Control (MAC) Protocol Data Units (MPDUs) to maximize the system throughput with satisfying the delay requirement of each queue when using the Aggregate MPDU (A-MPDU) aggregation in IEEE 802.11ac. The delay is defined as the sum of the queuing delay and the service delay. If few frames in a queue are aggregated, the frames which remain in the queue for next transmissions may violate the target delay because of the overhead for the next transmissions such as the backoff time, Physical Layer Convergence Procedure (PLCP) preamble, and PLCP header. If many of the frames in the queue are aggregated, the frames of the queue and the other queues may violate their target delays because of a long transmission duration and a long channel occupancy. In this paper, we obtain the average delay for each queue and the optimal number of aggregated MPDUs for the delay requirement of each queue in IEEE 802.11ac. At the last, we evaluate and show the performance of our proposed method through simulations. The simulation results show that the proposed method can estimate the average delay for each queue accurately. The simulation results also show that the proposed method can obtain the violation rates on the target delays less than 0.1. Furthermore, the simulation results show that the proposed method can yield higher system throughput than other conventional methods.