Brain tumor segmentation is one of the most challenging tasks of medical image analysis. The diagnosis of patients with gliomas is based on the analysis of magnetic resonance images and manual segmentation of tumor boundaries. However, due to its time-consuming nature, there is a need for a fast and reliable automatic segmentation algorithm. In recent years, deep learning methods applied to brain tumor segmentation have shown promising results. In this paper, a deep neural network model based on U-Net neural network architecture is proposed for brain glioma segmentation. It is proposed to use deep convolutional neural network models pre-trained on the ImageNet dataset as U-Net encoders. Among such models, VGG16, VGG19, Mobilenetv2, Inception, Efficientnetb7, InceptionResnetV2, DenseNet201, DenseNet121 were used. The computational experimental analysis performed in the paper on a set of MRI brain images showed that the best encoder model for the above deep models was the DenseNet121 model with the following values of segmentation metrics Mean IoU of 91.34 %, Mean Dice of 94.26 %, Accuracy of 94.22 %. The paper also comparatively analyses the results of the proposed segmentation method with several works of other authors. The comparative analysis of the segmentation results of the studied MRI images showed that the DenseNet121 model either surpassed or was comparable to the models proposed in the refereed papers in terms of segmentation accuracy metrics.