The accelerating rise of the amount of daily produced medical image data and the high costs of human expert training are strongly motivating the efforts dedicated to the development of reliable and efficient image segmentation and interpretation methodology. This paper proposes a fully automatic method to provide reliable segmentation of brain tissues from volumetric multi-spectral magnetic resonance image data. The proposed method provides a U-Net neural network based decision making, that is trained with infant brain MRI records originating from the iSeg-2017 challenge, which were preprocessed only to normalize the intensity histograms of individual records. The accuracy of the proposed method is evaluated using statistical indicators. The quality of the segmentation is characterized by overall correct decision rate exceeding 89%, and average Dice scores of 92.7%, 88.7%, and 87.0% for cerebro-spinal fluid, grey matter, and white matter, respectively.