In this paper, we propose an automatic design support system for compact acoustic devices such as microspeakers inside smartphones. The proposed design support system outputs the dimensions of compact acoustic devices with the desired acoustic characteristic. This system uses a deep neural network (DNN) to obtain the relationship between the frequency characteristic of the compact acoustic device and its dimensions. The training data are generated by the acoustic finite-difference time-domain (FDTD) method so that many training data can be easily obtained. We demonstrate the effectiveness of the proposed system through some comparisons between desired and designed frequency characteristics.