Three-dimensional (3D) point cloud registration is an important step in three-dimensional (3D) model reconstruction or 3D mapping. Currently, there are many methods for point cloud registration, but these methods are not able to simultaneously solve the problem of both efficiency and precision. We propose a fast method of global registration, which is based on RGB (Red, Green, Blue) value by using the four initial point pairs (FIPP) algorithm. First, the number of different RGB values of points in a dataset are counted and the colors in the target dataset having too few points are discarded by using a color filter. A candidate point set in the source dataset are then generated by comparing the similarity of colors between two datasets with color tolerance, and four point pairs are searched from the two datasets by using an improved FIPP algorithm. Finally, a rigid transformation matrix of global registration is calculated with total least square (TLS) and local registration with the iterative closest point (ICP) algorithm. The proposed method (RGB-FIPP) has been validated with two types of data, and the results show that it can effectively improve the speed of 3D point cloud registration while maintaining high accuracy. The method is suitable for points with RGB values.