Image registration is a fundamental task in medical image analysis. Recently, many deep learning based image registration methods have been extensively investigated due to their comparable performance with the state-of-the-art classical approaches despite the ultra-fast computational time. However, the existing deep learning methods still have limitations in the preservation of original topology during the deformation with registration vector fields. To address this issues, here we present a cycle-consistent deformable image registration, dubbed CycleMorph. The cycle consistency enhances image registration performance by providing an implicit regularization to preserve topology during the deformation. The proposed method is so flexible that can be applied for both 2D and 3D registration problems for various applications, and can be easily extended to multi-scale implementation to deal with the memory issues in large volume registration. Experimental results on various datasets from medical and non-medical applications demonstrate that the proposed method provides effective and accurate registration on diverse image pairs within a few seconds. Qualitative and quantitative evaluations on deformation fields also verify the effectiveness of the cycle consistency of the proposed method.