Accurate delineation of anatomical boundaries on prostate MR is crucial for cancer staging and standardized assessment. Unfortunately, manual prostate segmentation is time consuming and prone to inter-rater variability while existing automated segmentation software is expensive and inaccurate. We demonstrate a novel fully-automated zonal prostate segmentation method that is fast and accurate using a convolutional neural network. The network is trained using a dataset of 149 T2-weighted prostate MR volumes that were manually annotated by radiologists. Our method improves upon prior related work, achieving a full-gland Dice score of 0.92 and zonal Dice score of 0.88.