Medical image registration is one of the key processing steps for biomedical image analysis such as cancer diagnosis. Recently, deep learning based supervised and unsupervised image registration methods have been extensively studied due to its excellent performance in spite of ultra-fast computational time compared to the classical approaches. In this paper, we present a novel unsupervised medical image registration method that trains deep neural network for deformable registration of 3D volumes using a cycle-consistency. Thanks to the cycle consistency, the proposed deep neural networks can take diverse pair of image data with severe deformation for accurate registration. Experimental results using multiphase liver CT images demonstrate that our method provides very precise 3D image registration within a few seconds, resulting in more accurate cancer size estimation.