Aiming at the fast and accurate measurement of rail wear based on 3D structured light scanning, this paper proposes a point cloud registration algorithm based on 4PCS (4-points congruent sets) and SICP (sparse iterative closest point), which is used to quickly and accurately register the standard rail point cloud and incomplete worn rail point clouds with noise. Since the wear rail data obtained by one-time scanning of the three-dimensional structured light scanner is usually incomplete and contains noise, 4PCS with good robustness for low overlap point cloud registration is firstly used to coarse registration of the rail point cloud, which provides a good initial transformation matrix for accurate registration. Then, the SICP with good robustness for noisy point cloud registration is used for accurate registration. Finally, the rail head wear is calculated according to the accurate registration results. It quantitatively analyzes the influence of different levels of down-sampling on registration accuracy, time and calculation accuracy of rail head wear, which demonstrates the advantage of 4PCS and SICP in fast and accurate registration of incomplete and noisy rail point clouds. It is concluded that different levels of down-sampling have no influence on the calculation accuracy of rail head wear. Meanwhile, the robustness of SICP in accurate registration of worn rail point cloud with noise is verified by quantitative comparison analysis of the point cloud registrations with different levels of noise.