Three-dimensional (3-D) data have many applications in the field of computer vision and a point cloud is one of the most popular modalities. Therefore, how to establish a good representation for a point cloud is a core issue in computer vision, especially for 3-D object recognition tasks. Existing approaches mainly focus on the invariance of representation under the group of permutations. However, for point cloud data, it should also be rotation invariant. To address such invariance, in this article, we introduce a relation of equivalence under the action of rotation group, through which the representation of point cloud is located in a homogeneous space. That is, two point clouds are regarded as equivalent when they are only different from a rotation. Our network is flexibly incorporated into existing frameworks for point clouds, which guarantees the proposed approach to be rotation invariant. Besides, a sufficient analysis on how to parameterize the group SO(3) into a convolutional network, which captures a relation with all rotations in 3-D Euclidean space [Formula: see text]. We select the optimal rotation as the best representation of point cloud and propose a solution for minimizing the problem on the rotation group SO(3) by using its geometric structure. To validate the rotation invariance, we combine it with two existing deep models and evaluate them on ModelNet40 dataset and its subset ModelNet10. Experimental results indicate that the proposed strategy improves the performance of those existing deep models when the data involve arbitrary rotations.