The current partial overlapping point cloud registration algorithms have limitations in detecting overlapping boundary areas and eliminating non-overlapping points， which hinders the further enhancement of their performance. In order to address these issues， this study proposed a partially overlapping point cloud registration network driven by two-stage overlap scores and matching matrix. Firstly， the pose estimation module utilized neighborhood consistent features to estimate the initial pose for improved alignment accuracy. Secondly， a channel space perception Transformer module was designed to perceive two-point cloud overlapping regions to maintain accurate perception of overlapping boundary regions. Then， a feature encoder based on Transformer was proposed to encode the features of the point cloud after initial alignment， so as to excavate the feature map global and significant channel features. Finally， the cosine similarity matrix was transformed into a matching matrix using outlier removal method to correctly match corresponding points while removing overlapping points. The effectiveness of the proposed algorithm was validated on ModelNet40， ShapeNetCore.v2 and Stanford Bunny datasets. On ModelNet40 dataset， compared with sub-optimal algorithm GeoTransformer， MIE（R） and MAE（R） decrease by 12.79% and 9.78% respectively. On ShapeNetCore.v2 dataset， compared with sub-optimal algorithm MGFPCR， RMSE（R） and MAE（R） of the proposed algorithm decreased by 42.00% and 61.66%， respectively. On Stanford Bunny dataset， compared with sub-optimal algorithm ROPNet， RMSE（R） and MAE（R） of the proposed algorithm decreased by 25.53% and 5.58%， respectively. Experimental results demonstrate that the proposed algorithm outperforms other algorithms in terms of generalization performance and noise resistance.