Color consistency correction for color point clouds is a fundamental yet important task in 3D rendering and compression applications. In the past, most previous color correction methods aimed at correcting color for color images. The purpose of this paper is to propose a grouping-based hybrid color correction algorithm for color point clouds. Our algorithm begins by estimating the overlapping rate between the aligned source and target point clouds, and then adaptively partitions the target points into two groups, namely the close proximity group Gcl and the moderate proximity group Gmod, or three groups, namely Gcl, Gmod, and the distant proximity group Gdist, when the estimated overlapping rate is low or high, respectively. To correct color for target points in Gcl, a K-nearest neighbors based bilateral interpolation (KBI) method is proposed. To correct color for target points in Gmod, a joint KBI and the histogram equalization (JKHE) method is proposed. For target points in Gdist, a histogram equalization (HE) method is proposed for color correction. Finally, we discuss the grouping-effect free property and the ablation study in our algorithm. The desired color consistency correction benefit of our algorithm has been justified through 1086 testing color point cloud pairs against the state-of-the-art methods. The C++ source code of our algorithm can be accessed from the website: https://github.com/ivpml84079/Point-cloud-color-correction.