The work consists in recognizing the gestures of the alphabet in Peruvian sign language using techniques of digital image processing and a model of Deep Learning (CNN). Image processing techniques are used for segmentation and tracking of the hand of the person making the gestures. Once the image of the segmented hand is used, a CNN classification model is used to be able to recognize the gesture. The image processing and CNN algorithms were implemented in the Python programming language. The database used was 23,000 images divided into 70% for training, 15% for testing and 15% for validation. Likewise, said data corresponds to 1000 images for each non-mobile gesture of the alphabet. The results obtained for the precision of the classifier were 99.89, 99.88 and 99.85% for the data of training, test and validation respectively. In the case of the Log Loss parameter, 0.0132, 0.0036, and 0.0107 were obtained for the training, testing and validation data, respectively.