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Various image filtering strategies have been effective, but most algorithms are to fail in general and create artifacts or remove image fine structures. Hence we propose a novel image filter based on grey polynomial model(GPM) to reduce image noise. The basic conceptions of grey polynomial model are described. The new image filter adopts each noisy pixel's neighborhoods to rectify its intensity value. In addition, the QR decomposition is used to enhance the algorithm's robustness. The experimental results demonstrate that the proposed algorithm, can do better than some more popular denoising methods, such as the median filter and GM(1,1) model, on the removal of low-density impulse noise. Finally, the improved algorithm can effectively eliminate image noise and achieve better denoising effect from both subjective and objective aspects, while preserve the image's textures and edges.