In order to have the advantages of edge protecting and high efficiency of traditional methods of image de noising, according to the correlation of image’s space pixels, the paper has designed the local polynomial approximation function, analyzed the local approximation theoretically and established the algorithm of local polynomial approximation (LPA).For the noise image, first, made the polynomial fitting for the image pixel, structured the local polynomial approximation function. Second, used intersection of confidence intervals (ICI) rule to select the ideal scale of the local polynomial adaptively. Finally, adopted the algorithm of LPA to de noise the Gaussian noisy image. Experimental results show that the algorithm inherits the traditional isotropic de noising algorithms advantage of high efficiency and makes up for the anisotropy de noising algorithms shortcomings that the computation time is too long, so it cant meet the needs of the real time requirement.