With the development of three-dimensional sensing technology, the data volume of point cloud grows rapidly. Therefore, point cloud is usually down-sampled in advance so as to save memory space and reduce the computational complexity for its downstream processing tasks such as classification, segmentation, reconstruction in learning based point cloud processing. Obviously, the sampled point clouds should be well representative and maintain the geometric structure of the original point clouds so that the downstream tasks can achieve satisfied performance based on the point clouds sampled from the original ones. Traditional point cloud sampling methods such as farthest point sampling and random sampling mainly heuristically select a subset of the original point cloud. However, they do not make full use of high-level semantic representation of point clouds, are sensitive to outliers. Some of other sampling methods are task oriented. In this paper, a Universal Point cloud Sampling Network without knowing downstream tasks (denoted as UPSNet) is proposed. It consists of three modules. The importance learning module is responsible for learning the mutual information between the points of input point cloud and calculating a group of variational importance probabilities to represent the importance of each point in the input point cloud, based on which a mask is designed to discard the points with lower importance so that the number of remaining points is controlled. Then, the regional learning module learns from the input point cloud to get the high dimensional space embedding of each region, and the global feature of each region are obtained by weighting the high dimensional space embedding with the variational importance probability. Finally, through the coordinate regression module, the global feature and the high dimensional space embedding of each region are cascaded for learning to obtain the sampled point cloud. A series of experiments are implemented in which the point cloud classification, segmentation, reconstruction and retrieval are performed on the reconstructed point clouds sampled with different point cloud sampling methods. The experimental results show that the proposed UPSNet can provide more reasonable sampling result of the input point cloud for the downstream tasks of classification, segmentation, reconstruction and retrieval, and is superior to the existing sampling methods without knowing the downstream tasks. The proposed UPSNet is not oriented to specific downstream tasks, so it has wide applicability.