This article is devoted to the development of a computer system for leukocytes classification on blood cell images. Solving of the white blood cells classification task makes it possible to diagnose not only blood diseases, but also a wide range of other diseases, as well as to evaluate the overall functional state of human health. Current leukocytes classification methods and ways have a fairly large number of drawbacks, which make the problem of finding the optimal and effective method as a tool to solve this classification task. In this developed computer system, we use the method based on the using of a trained convolutional neural network as a binary classifier for leukocytes classification. The article shows the advantage of using this architecture and deep learning technology to solve objects classification task on digital images. The developed system allows in most cases correctly and with a high speed to determine whether the white blood cell belongs to one of the two classes, which indicates the possibility of using this system as auxiliary tool for blood hematological analysis.