Image inpainting aims to fill the missing hole of the input. It is hard to solve this task efficiently when facing high-resolution images due to two reasons: (1) Large reception field needs to be handled for high-resolution image inpainting. (2) The general encoder and decoder network synthesizes many background pixels synchronously due to the form of the image matrix. In this paper, we try to break the above limitations for the first time thanks to the recent development of continuous implicit representation. In detail, we downsample and encode the degraded image to produce the spatial-adaptive parameters for each spatial patch via an attentional Fast Fourier Convolution (FFC)-based parameter generation network. Then, we take these parameters as the weights and biases of a series of multi-layer perceptron (MLP), where the input is the encoded continuous coordinates and the output is the synthesized color value. Thanks to the proposed structure, we only encode the high-resolution image in a relatively low resolution for larger reception field capturing. Then, the continuous position encoding will be helpful to synthesize the photo-realistic high-frequency textures by re-sampling the coordinate in a higher resolution. Also, our framework enables us to query the coordinates of missing pixels only in parallel, yielding a more efficient solution than the previous methods. Experiments show that the proposed method achieves real-time performance on the 2048×2048 images using a single GTX 2080 Ti GPU and can handle 4096×4096 images, with much better performance than existing state-of-the-art methods visually and numerically. The code is available at: https://github.com/NiFangBaAGe/CoordFill. Copyright © 2023, Association for the Advancement of Artificial Intelligence (www.aaai.org).