Chronic wounds are ulcerations of the skin that fail to heal because of an underlying condition such as diabetes mellitus or venous insufficiency. The timely identification of this condition is crucial for healing. However, this identification requires expert knowledge unavailable in some care situations. Here, artificial intelligence technology may support clinicians. In this study, we explore the performance of a deep convolutional neural network to classify diabetic foot and venous leg ulcers using wound images. We trained a convolutional neural network on 863 cropped wound images. Using a hold-out test set with 80 images, the model yielded an F1-score of 0.85 on the cropped and 0.70 on the full images. This study shows promising results. However, the model must be extended in terms of wound images and wound types for application in clinical practice.