We propose a method for speeding up a 3D point cloud registration through a cascading feature extraction. The current approach with the highest accuracy is realized by iteratively executing feature extraction and registration using deep features. However, iterative feature extraction takes time. Our proposed method significantly reduces the computational cost using cascading shallow layers. Our idea is to omit redundant computations that do not always contribute to the final accuracy. The proposed approach is approximately three times faster than the existing methods without a loss of accuracy.