Alpha-decay events in a nuclear emulsion are standard calibration sources for the relation between the track length and the kinetic energy in each emulsion sheet. We developed an efficient classifier that sorts such alpha-decay events from various vertex-like objects in an emulsion using a convolutional neural network (CNN). We trained the CNN using 15885 images of vertex-like objects, including 906 alpha-decay events, and tested it using a dataset of 46948 images including 255 alpha-decay events. The precision and recall scores of the classification using the previous method without a CNN for the same dataset were 0.081 ± 0.006 and 0.788 ± 0.056, respectively. In contrast, our trained models achieved an average precision score of 0.760 ± 0.006 for the test dataset, after extensively tuning the hyperparameters of the CNN. Moreover, for the model obtained, the discrimination threshold of the classification can be adjusted arbitrarily according to the trade-off between the precision and recall scores. Furthermore, the developed classifier obtained a precision of 0.571 ± 0.017 when the recall score was assigned a value of 0.788. Finally, the developed CNN method reduced the need for additional human visual inspection, required after classification, by a factor of approximately 1/7, compared to the former method without a CNN, proving the feasibility of the proposed classifier.