As interest in point cloud processing has gradually increased in the industry, point cloud sampling techniques have been researched to improve deep learning networks. As many conventional models use point clouds directly, the consideration of computational complexity has become critical for practicality. One of the representative ways to decrease computations is downsampling, which also affects the performance in terms of precision. Existing classic sampling methods have adopted a standardized way regardless of the task-model property in learning. However, this limits the improvement of the point cloud sampling network’s performance. That is, the performance of such task-agnostic methods is too low when the sampling ratio is high. Therefore, this paper proposes a novel downsampling model based on the transformer-based point cloud sampling network (TransNet) to efficiently perform downsampling tasks. The proposed TransNet utilizes self-attention and fully connected layers to extract meaningful features from input sequences and perform downsampling. By introducing attention techniques into downsampling, the proposed network can learn about the relationships between point clouds and generate a task-oriented sampling methodology. The proposed TransNet outperforms several state-of-the-art models in terms of accuracy. It has a particular advantage in generating points from sparse data when the sampling ratio is high. We expect that our approach can provide a promising solution for downsampling tasks in various point cloud applications.