Image denoising is a fundamental problem in computer vision and multimedia computation. Non-local filters are effective for image denoising. But existing deep learning methods that use non-local computation structures are mostly designed for high-level tasks, and global self-attention is usually adopted. For the task of image denoising, they have high computational complexity and have a lot of redundant computation of uncorrelated pixels. To solve this problem and combine the marvelous advantages of non-local filter and deep learning, we propose a Convolutional Unbiased Regional (CUR) transformer. Based on the prior that, for each pixel, its similar pixels are usually spatially close, our insights are that (1) we partition the image into non-overlapped windows and perform regional self-attention to reduce the search range of each pixel, and (2) we encourage pixels across different windows to communicate with each other. Based on our insights, the CUR transformer is cascaded by a series of convolutional regional self-attention (CRSA) blocks with U-style short connections. In each CRSA block, we use convolutional layers to extract the query, key, and value features, namely Q , K , and V , of the input feature. Then, we partition the Q , K , and V features into local non-overlapped windows and perform regional self-attention within each window to obtain the output feature of this CRSA block. Among different CRSA blocks, we perform the unbiased window partition by changing the partition positions of the windows. Experimental results show that the CUR transformer outperforms the state-of-the-art methods significantly on four low-level vision tasks, including real and synthetic image denoising, JPEG compression artifact reduction, and low-light image enhancement.