For 3D point cloud registration, how to improve the local feature correlation of two point clouds is a challenging problem. In this paper, we propose a cascaded mutual information attention registration network. The network improves the accuracy of point cloud registration by stacking residual structure and using lateral connection. Firstly, the local reference coordinate system is defined by spherical representation for the local point set, which improves the stability and reliability of local features under noise. Secondly, the attention structure is used to improve the network depth and ensure the convergence of the network. Furthermore, a lateral connection is introduced into the network to avoid the loss of features in the process of concatenation. In the experimental part, the results of different algorithms are compared. It can be found that the proposed cascaded network can enhance the correlation of local features between different point clouds. As a result, it improves the registration accuracy significantly over the DCP and other typical algorithms.