To improve accuracy， robustness， and generalization of point cloud registration and address the problem of the Iterative Closest Point （ICP） algorithm easily falling into local optimal solution， a point cloud registration method of coordinate Geometric Sampling based on Deep Closest Point （GSDCP） was proposed. Firstly， the central point curvature was estimated using coordinates of surrounding points of each point， and points that preserved geometric features of the point cloud were selected through curvature sizes， so as to realize downsampling of the point cloud. Secondly， a Dynamic Graph Convolutional Neural Network （DGCNN） was employed to coordinate with the downsampled point cloud to learn point cloud features that incorporated local geometry information， and contextual information was captured using a Transformer， and soft Pointers facilitate approximate combination and matching between two feature embedders. Finally， a differentiable Single Value Decomposition （SVD） layer was utilized to estimate the final rigid transformation. Point cloud registration experimental results on ModelNet40 dataset show that compared with ICP， Globally optimal ICP （Go-ICP）， PointNetLK， Fast Global Registration （FGR）， ADGCNNLK （Attention Dynamic Graph Convolutional Neural Network Lucas-Kanade）， Deep Closest Point （DCP）， and Multi-Features Guidance Network （MFGNet）， GSDCP achieves all the best registration accuracy and robustness in scenarios with or without noise， as well as when the point cloud category is invisible. In noise-free scenario， GSDCP reduces rotational Mean Square Error （MSE） by 31.3% and translational MSE by 58.3% compared to MFGNet. In noisy scenario， GSDCP reduces rotational MSE by 33.9% and translational MSE by 73.4% compared to MFGNet. When the point cloud category is invisible， GSDCP reduces rotational MSE by 57.7% and translational MSE by 77.9% compared to MFGNet. Additionally， when dealing with incomplete point cloud data （including random occlusion and fragmentary point cloud）， GSDCP exhibits reductions of 35.1% in rotational MSE and 39.8% in translational MSE compared to MFGNet when point cloud integrity is below 75%.