While deep convolutional neural networks (CNNs) have achieved remarkable success in 2D medical image segmentation, it is still a difficult task for CNNs to segment important organs or structures from 3D medical images owing to several mutually affected challenges, including the complicated anatomical environments in volumetric images, optimization difficulties of 3D networks and inadequacy of training samples. In this paper, we present a novel and efficient 3D fully convolutional network equipped with a 3D deep supervision mechanism to comprehensively address these challenges; we call it 3D DSN. Our proposed 3D DSN is capable of conducting volume-to-volume learning and inference, which can eliminate redundant computations and alleviate the risk of over-fitting on limited training data. More importantly, the 3D deep supervision mechanism can effectively cope with the optimization problem of gradients vanishing or exploding when training a 3D deep model, accelerating the convergence speed and simultaneously improving the discrimination capability. Such a mechanism is developed by deriving an objective function that directly guides the training of both lower and upper layers in the network, so that the adverse effects of unstable gradient changes can be counteracted during the training procedure. We also employ a fully connected conditional random field model as a post-processing step to refine the segmentation results. We have extensively validated the proposed 3D DSN on two typical yet challenging volumetric medical image segmentation tasks: (i) liver segmentation from 3D CT scans and (ii) whole heart and great vessels segmentation from 3D MR images, by participating two grand challenges held in conjunction with MICCAI. We have achieved competitive segmentation results to state-of-the-art approaches in both challenges with a much faster speed, corroborating the effectiveness of our proposed 3D DSN.