Point cloud upsampling can provide a dense and uniform representation, which is crucial for improving the quality of 3D reconstruction. While many traditional and deep learning methods of point cloud upsampling have been proposed, their performance need to be further improved. Additionally, most of the existing methods are networks with a single sampling rate, which is inefficient and inconvenient in practical applications. To address these limitations, we propose an arbitrary-rate upsampling network based on a lightweight Transformer for 3D point cloud in this paper. First, a Light-Transformer with skip-attention is designed to extract point cloud features, this method not only has a strong learning ability, but also saves computing and storage resources. Then, after expanding features using 2D grid mechanism and shuffle operation, a coordinate regression module with residual refinement unit is designed to rectify and obtain the precise upsampled point cloud. Next, through the proposed upsampling network based on Light-Transformer, the upsampled point cloud with the maximum sampling rate can be getted, followed by Farthest Point Sampling, we can obtain the point cloud with arbitrary sampling rate. Extensive experiments demonstrate that our proposed method achieves superior upsampling performance, and achieves arbitrary-rate point cloud upsampling.