With the development of advanced technologies, the problem of information security is becoming increasingly relevant. Given the development of spyware and digital technology allow more effective attacks on computer systems, including corporate networks, confidentiality can only be achieved through the creation of comprehensive information security. And one of the main elements of such a security system is the subsystem, which provides the identification of the user of the computer. Traditional identification and authentication methods based on the use of cards, electronic keys or other portable identifiers, as well as passwords and access codes, have significant disadvantages. The main disadvantage of such methods is the ambiguity of the identified person. Existing methods of user identification by keyboard handwriting are accurate from 78 % to 93,59 % and built on multilevel neural networks, which affects the speed of their learning and as a result of the cost of more resources, so it is actual to increase the accuracy of identification and reduce the time to train the neural network and design the appropriate method. An experimental study was made of the possibility of using a two-level neural network with a built-in sigmoid activation function to improve the accuracy of user identification by keyboard handwriting and proposed a method based on this mathematical apparatus. A comparison of the proposed identification method with existing ones was also performed, which showed an increase in the accuracy of user identification by 1–15 %. The method of Saket Maheshwari and Vikram Pudi has similar accuracy indicators, but there are several significant differences between the proposed and the existing method: in their work Saket Maheshwari and Wikam Pudi used a five-level neural network; it took 9 minutes to study their neural network. In the proposed method, the time of training the neural network is 6 minutes, which is faster for 3 minutes and, as a result, is much more effective when used, since the user's identification time is reduced and high identification accuracy is on the same high level.