3D medical image registration is of great clinical importance. However, supervised learning methods require a large amount of accurately annotated corresponding control points (or morphing). The ground truth for 3D medical images is very difficult to obtain. Unsupervised learning methods ease the burden of manual annotation by exploiting unlabeled data without supervision. In this paper, we propose a new unsupervised learning method using convolutional neural networks under an end-to-end framework, Volume Tweening Network (VTN), to register 3D medical images. Three technical components ameliorate our unsupervised learning system for 3D end-to-end medical image registration: (1) We cascade the registration subnetworks; (2) We integrate affine registration into our network; and (3) We incorporate an additional invertibility loss into the training process. Experimental results demonstrate that our algorithm is 880x faster (or 3.3x faster without GPU acceleration) than traditional optimization-based methods and achieves state-of-the-art performance in medical image registration.