This paper proposes a convolutional neural network (CNN)-based deep learning model for predicting the difficulty of extracting a mandibular third molar using a panoramic radiographic image. The applied dataset includes a total of 1053 mandibular third molars from 600 preoperative panoramic radiographic images. The extraction difficulty was evaluated based on the consensus of three human observers using the Pederson difficulty score (PDS). The classification model used a ResNet-34 pretrained on the ImageNet dataset. The correlation between the PDS values determined by the proposed model and those measured by the experts was calculated. The prediction accuracies for C1 (depth), C2 (ramal relationship), and C3 (angulation) were 78.91%, 82.03%, and 90.23%, respectively. The results confirm that the proposed CNN-based deep learning model could be used to predict the difficulty of extracting a mandibular third molar using a panoramic radiographic image.