This article discusses the design and development of a neural network algorithm for the segmentation of text areas in real-scene images. After reviewing the available neural network models, the U-net model was chosen as a basis. Then an algorithm for detecting text areas in real-scene images was proposed and implemented. The experimental training of the network allows one to define the neural network parameters such as the size of input images and the number and types of the network layers. Bilateral and low-pass filters were considered as a preprocessing stage. The number of images in the KAIST Scene Text Database was increased by applying rotations, compression, and splitting of the images. The results obtained were found to surpass competing methods in terms of the F-measure value.