Brain tumor segmentation plays a key role in tumor diagnosis and surgical planning. In this paper, we propose a solution to the 3D brain tumor segmentation problem using deep learning and graph cut from the MRI data. In particular, the probability maps of a voxel to belong to the object (tumor) and background classes from the UNet are used to improve the energy function of the graph cut. We derive new expressions for the data term, the region term and the weight factor balancing the data term and the region term for individual voxels in our proposed model. We validate the performance of our model on the publicly available BRATS 2018 dataset. Our segmentation accuracy with a dice similarity score of 0.92 is found to be higher than that of the graph cut and the UNet applied in isolation as well as over a number of state of the art approaches.