Point cloud registration is a foundational task for 3D alignment and reconstruction applications. While both traditional and learning-based registration approaches have succeeded, leveraging the intrinsic symmetry of point cloud data, including rotation equivariance, has received insufficient attention. This prohibits the model from learning effectively, resulting in a requirement for more training data and increased model complexity. To address these challenges, we propose a graph neural network model embedded with a local Spherical Euclidean 3D equivariance property through \(\textbf{SE}\) (3) message passing based propagation. Our model is composed mainly of a descriptor module, equivariant graph layers, match similarity, and the final regression layers. Such modular design enables us to utilize sparsely sampled input points and initialize the descriptor by self-trained or pre-trained geometric feature descriptors easily. Experiments conducted on the 3DMatch and KITTI datasets exhibit the compelling and robust performance of our model compared to state-of-the-art approaches, while the model complexity remains relatively low at the same time.