In this paper, an approach to solving the problem of detecting skin malignancies, namely, melanoma, based on the analysis of dermoscopic images using the methods of deep learning. For this purpose, a deep convolutional neural network architecture was developed, which was applied to the processing of dermoscopic images of various skin lesions contained in the HAM10000 data set. The studied data was previously processed to eliminate noise, contamination, and change the size and format of images. In addition, since the disease classes are unbalanced, a number of transformations were performed to balance them. The data obtained in this way were divided into two classes: Melanoma and Benign. Computer experiments on the use of a built deep neural network on the data obtained in this way have shown that the proposed approach provides an accuracy of 91% on the test sample, which exceeds similar results obtained by other algorithms.