In recent years, since the solution of permutation invariance of point cloud, point cloud based deep learning methods have achieved great breakthrough. Point cloud is adopted as input data to describe 3D objects and then neural network is employed to extract features from the point cloud. However, the existing methods cannot solve the rotation-invariance problem, thus existing models are of poor robustness against rotation. Meanwhile, the existing methods merely design the hierarchical structure of neural network by prior knowledge and none of them have made effort to explore the geometric structure underlying the point cloud, which is prone to cause lower capacity of network. For these reasons, a point cloud representation with rotation-invariance and a hierarchical cluster network are proposed, attempting to solve the above two problems in both theoretical and practical ways. Extensive experiments have shown that the proposed method greatly outperforms the state-of-the-arts in rotation robustness on rotation-augmented 3D object classification, object part segmentation, object semantic segmentation benchmarks.