In this work, fully automatic binary segmentation of GBMs (glioblastoma multiforme) in 2D magnetic resonance images is presented using a convolutional neural network trained exclusively on synthetic data. The precise segmentation of brain tumors is one of the most complex and challenging tasks in clinical practice and is usually done manually by radiologists or physicians. However, manual delineations are time-consuming, subjective and in general not reproducible. Hence, more advanced automated segmentation techniques are in great demand. After deep learning methods already successfully demonstrated their practical usefulness in other domains, they are now also attracting increasing interest in the field of medical image processing. Using fully convolutional neural networks for medical image segmentation provides considerable advantages, as it is a reliable, fast and objective technique. In the medical domain, however, only a very limited amount of data is available in the majority of cases, due to privacy issues among other things. Nevertheless, a sufficiently large training data set with ground truth annotations is required to successfully train a deep segmentation network. Therefore, a semi-automatic method for generating synthetic GBM data and the corresponding ground truth was utilized in this work. A U-Net-based segmentation network was then trained solely on this synthetically generated data set. Finally, the segmentation performance of the model was evaluated using real magnetic resonance images of GBMs.