A deep-learning-based acoustic eigenvalue analysis method is proposed for predicting the acoustic natural modes and natural frequencies of a double cavity such as a passenger compartment cavity connected to a trunk cavity. A double cavity comprises a main cavity, auxiliary cavity, and perforated partition between them. The hole distribution in the perforated partition strongly affects the acoustic characteristics of the double cavity. For a given hole distribution, a single deep learning model was developed for predicting the acoustic natural modes and natural frequencies of a double cavity simultaneously. The deep learning model was developed based on convolutional and transposed convolutional neural layers. The model was trained, validated, and tested using a suitable dataset for a two-dimensional double cavity and then extended to a three-dimensional simplified passenger compartment cavity connected to a trunk cavity. The validity of the extended model was verified for simplified acoustic cavities of commercial sedans. The latent variables of the model exhibited a changing trend of the natural frequencies depending on the hole distribution. Gradient-weighted class activation mapping was used to visualize important locations that significantly affect the output of the proposed model.