Although Iterative Closest Point(ICP) algorithm and its variant are the basic method for 3D point cloud rigid body registration, the point cloud iteration-based registration method get low convergence efficiency, severely constraining registration efficiency. In this paper, the Frobenius norm property is employed to represent error function between source point cloud and target point cloud, and due to the property of the Frobenius norm, the closest distance between 2 point clouds can be converted into a single calculation form to get transformation matrix. This method greatly reduce iteration times and registration time. The experiment in this paper is compared with three classical ICP algorithms and three learning-based algorithms on the Standford dataset and 3DMatch dataset respectively, and the registration time of fast ICP is less than that of other algorithms. When the registration accuracy is similar, the fast ICP method only has 20% of the iteration times of the traditional ICP algorithm, and 1/4 times the registration time on the Standford dataset, 1/8 times on the 3DMatch dataset of the traditional ICP algorithm. The fast ICP algorithm is more efficient when the amount of points is large.