The present work proposes to recognize the static hand gestures taken under invariations features as scale, rotation, translation, illumination, noise and background. We use the alphabet of sign language of Peru (LSP). For this purpose, digital image processing techniques are used to eliminate or reduce noise, to improve the contrast under a variant illumination, to separate the hand from the background of the image and finally detect and cut the region containing the hand gesture. We use of convolutional neural networks (CNN) to classify the 24 hand gestures. Two CNN architectures were developed with different amounts of layers and parameters per layer. The tests showed that the first CNN has an accuracy of 95.37% and the second CNN has an accuracy of 96.20% in terms of recognition of the 24 static hand gestures using the database developed. We compared the two architectures developed in accuracy level for each type of invariance presented in this paper. We compared the two architectures developed and usual techniques of machine learning in results of accuracy.