Benefiting from powerful convolutional neural networks (CNNs), learning-based image inpainting methods have made significant breakthroughs over the years. However, some nature of CNNs (e.g. local prior, spatially shared parameters) limit the performance in the face of broken images with diverse and complex forms. Recently, a class of attention-based network architectures, called transformer, has shown significant performance on natural language processing fields and high-level vision tasks. Compared with CNNs, attention operators are better at long-range modeling and have dynamic weights, but their computational complexity is quadratic in spatial resolution, and thus less suitable for applications involving higher resolution images, such as image inpainting. In this paper, we design a novel attention linearly related to the resolution according to Taylor expansion. And based on this attention, a network called $T$-former is designed for image inpainting. Experiments on several benchmark datasets demonstrate that our proposed method achieves state-of-the-art accuracy while maintaining a relatively low number of parameters and computational complexity. The code can be found at \href{https://github.com/dengyecode/T-former_image_inpainting}{github.com/dengyecode/T-former\_image\_inpainting}

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