Recent past has seen an inexorable shift towards the use of deep learning techniques to solve a myriad of problems in the field of medical imaging. In this paper, a novel segmentation method involving a fully-connected deep neural network called Deep Segmentation Network (DSN) is proposed to perform supervised regression for brain extraction from T1-weighted magnetic resonance (MR) images. In contrast to the existing patch-based feature learning techniques, DSN works on full 3D volumes, simplifying pre- and postprocessing operations, to efficiently provide a voxel-wise binary mask delineating the brain region. The model is evaluated using three publicly available datasets and is observed to either outdo or perform comparably to the state-of-the-art methods. DSN is able to achieve a maximum and minimum Dice Similarity Coefficient (DSC) of 97:57 and 92:82 respectively across all the datasets. Experiments conducted in this paper highlight the ability of the DSN model to automatically learn feature representations; making it a simple yet highly effective approach for brain segmentation. Preliminary experiments also suggest that the proposed model has the potential to segment sub-cortical structures accurately.