Point cloud registration has a wide range of applications in 3D reconstruction, pose estimation, intelligent driving, heritage conservation, and digital cities. The traditional iterative closest point (ICP) algorithm has strong dependence on the initial position, poor robustness, and low timeliness. To address the above issues, a fast point cloud registration method that incorporates RGB image information is proposed. The SIFT algorithm is used to detect feature points of point clouds corresponding to the RGB image, followed by feature point matching. The RANSAC algorithm is applied to remove erroneous point pairs in order to calculate the initial transformation matrix. After applying a pass-through filter for noise reduction and transiting down with a voxel grid, the point cloud is subjected to rotation and translation transformation for initial registration. On the basis of initial alignment, the FR-ICP algorithm is utilized for achieving precise registration. This method not only avoids the problem of ICP easily getting stuck in local optima, but also has higher registration accuracy and efficiency. Experimental studies were conducted based on point clouds of automotive parts collected in real scenes, and the results showed that the proposed method has a registration error of only 0.487 mm. Among the same group of experimental point clouds with comparable registration error, the proposed method showed a speed improvement of 69%/48% compared to ICP/FR-ICP with regard to registration speed.