3D point cloud has been widely used in applications such as self-driving cars, robotics, CAD models, etc. To the best of our knowledge, these applications raised the issue of privacy leakage in 3D point clouds, which has not been studied well. Different from the 2D image privacy, which is related to texture and 2D geometric structures, the 3D point cloud is texture-less and only relevant to 3D geometric structures. In this work, we defined the 3D point cloud privacy problem and proposed an efficient privacy-preserving framework named PointFlowGMM that can support downstream classification and segmentation tasks without seeing the original data. Using a flow-based generative model, the point cloud is projected into a latent Gaussian mixture-distributed subspace. We further designed a novel angular similarity loss to obfuscate the original geometric information and reduce the model size from 767MB to 120MB without a decrease in recognition performance. The projected point cloud in the latent space is orthogonally rotated randomly to protect original geometric structure, the class to class relationship is preserved after rotation, thus, the protected point cloud can support recognition task. We evaluated our model on multiple datasets and achieved comparable recognition results on encrypted point clouds compared to the original point clouds.