Image registration is one of the key processing steps for biomedical image analysis such as diagnosis of disease. 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. Most of the deep learning algorithms are designed to ensure diffeomorphism for the registration in calculating the deformation vector field. In this paper, based on the observation that a homeomorphic mapping between two topological spaces is as powerful as a diffeomorphism in ensuring the topology preservation and one-to-one mapping, we present a novel unsupervised medical image registration method that trains deep neural network to deform a 3D volume by homeomorphic mapping using a cycle-consistency. Using difficult multiphase liver registration tasks, we evaluate target registration error for the deformed images and demonstrate that the proposed method can provide accurate 3D image registration within a few seconds.