Most existing point cloud registration methods often ignore the relationship between neighboring nodes in the neighborhood， resulting in insufficient feature extraction of local geometric structures. To solve this problem， a Neighborhood-Attention and Topology-Aware graph convolution （NATA） method for robust point cloud registration was proposed to capture deeper semantic features and richer geometric information. Firstly， a cascade geometry-aware module was designed， which used a self-attention-based local neighborhood update graph convolution module to focus on the intrinsic geometric structure of local graphs， thereby obtaining more accurate local topological information. Secondly， a cascade structure combined various levels of local topological information to produce a more discriminative collection of local descriptors. Finally， a feature interaction-graph update module was proposed， which created an attention mechanism in the point clouds to capture their implicit relationships and perceive shape features of the point clouds. Experimental results on a challenging 3D point cloud benchmark test show that the proposed method achieves excellent Mean Absolute Error （MAE） of 0.157 2 and 0.154 4 for partial noisy point clouds registration under unknown shapes and unknown categories， respectively.