How to extract significant point cloud features and estimate the pose between them remains a challenging question, due to the inherent lack of structure and ambiguous order permutation of point clouds. Despite significant improvements in applying deep learning-based methods for most 3D computer vision tasks, such as object classification, object segmentation and point cloud registration, the consistency between features is still not attractive in existing learning-based pipelines. In this paper, we present a novel learning-based alignment network for complex alignment scenes, titled deep feature consistency and consisting of three main modules: a multiscale graph feature merging network for converting the geometric correspondence set into high-dimensional features, a correspondence weighting module for constructing multiple candidate inlier subsets, and a Procrustes approach named deep feature matching for giving a closed-form solution to estimate the relative pose. As the most important step of the deep feature matching module, the feature consistency matrix for each inlier subset is constructed to obtain its principal vectors as the inlier likelihoods of the corresponding subset. We comprehensively validate the robustness and effectiveness of our approach on both the 3DMatch dataset and the KITTI odometry dataset. For large indoor scenes, registration results on the 3DMatch dataset demonstrate that our method outperforms both the state-of-the-art traditional and learning-based methods. For KITTI outdoor scenes, our approach remains quite capable of lowering the transformation errors. We also explore its strong generalization capability over cross-datasets.