Passive acoustic monitoring (PAM) has emerged as an effective tool for studying underwater soundscapes and monitoring marine organisms. In this study, the biological sounds of three fish species that mainly inhabit or occur in the Korean coastal oceans, brown croaker (Miichthys miiuy), Pacific cod (Gadus macrocephalus), and small yellow croaker (Larimichthys polyactis) were recorded using the PAM method. The possibility of automatic classification was evaluated using a deep learning-based convolutional neural network (CNN) model based on the measured data. The biological fish sounds were recorded using hydrophones in the sea cage environments. The three fish species data were converted into spectrogram images and used as input for training and evaluating the CNN model. Gaussian noise was added to the test data to simulate low signal-to-noise ratio (SNR) environments. The model achieved high classification performance, with F1-score of about 96% on raw data and about 77% accuracy under signal-to-noise ratio conditions. These results suggest that CNN-based models be adequate for fish sound classification, even in acoustically complex underwater environments. Applying CNN models to classify and detect fish sounds can improve the automation and efficiency of PAM-based acoustic analysis, thereby improving the monitoring of fish populations, resource assessment, and ecological management in the future.