With the continuous development of 3D laser scanning technology, point clouds can quickly and intuitively obtain real-world information. Point cloud registration can solve the limitation that a single data source cannot fully reflect objective things. However, the partial overlap and the difficulty in identifying matchable and repeatable corresponding points lead to a large number of outliers and low registration accuracy. To address these issues, we propose a relative geometric-driven registration network with virtual correspondences (VRGNet). First, robust features between scenes are extracted through self-attention and cross-attention mechanisms. The virtual point generation (VPG) module is used to optimize point cloud position information and improve the point matching probability in overlapping areas. Then, combine the original and generated point clouds to learn rotation-invariant geometric features through relative geometric embedding (RGE). Finally, the coarse-to-fine point matching method is used to obtain reliable correspondences and high-precision transformation matrices. We conduct extensive testing on the large-scale outdoor KITTI dataset. The experimental results demonstrate that our method achieves higher efficiency and registration accuracy.