Due to the low efficiency and large error of traditional point cloud registration methods, this paper proposes a point cloud coarse registration method that is transformed in stages along with the vertical and horizontal directions. The proposed method first decentralizes the point clouds P and Q for coinciding the center points of two point clouds, then finds the feature point by traversing the distance from the center of mass, and rotates it to the y axis to complete the vertical alignment. The proposed method then finds the feature point again in the xOz plane by traversing the distance from the center of mass and rotates it around the y axis to align horizontally. Finally, to complete the registration, we use the iterative closest point fine registration algorithm. The proposed method has linear time complexity and constant space complexity, with no iterative computation. The proposed method is compared to three classical methods, and three groups of point clouds with varying numbers and scales are used. The experiment shows that the proposed method has high robustness for various point clouds. The proposed method has a registration time of about 4 s and a small change range; when compared to the three traditional methods, the time consumption is reduced by more than 50%. At the same time, the root mean square error of the proposed method is about 10^-8 mm, which maintains a good accuracy.