In order to remove the Gaussian noise in the infrared image while preserving and restoring the textures, edges and detailed features of the image, an infrared image denoising method based on dual density complex wavelet and coefficient correlation is proposed. This method makes the most of the advantages of dual density dual tree complex wavelet in image processing: translation invariance of image information, multi-directional selectivity of image texture and detail, etc. Based on the assumption of the distribution of image wavelet coefficients, according to the correlation between the current wavelet coefficient and its parent and child wavelet coefficients, Bayesian estimation is made for the noiseless wavelet coefficients to restore the noiseless infrared image. Finally, the denoised image is subjected to guided filter, so as to remove the ripple effect. Experimental data show that this method is superior to some existing algorithms in EPI, FSIM and visual effect of image, which proves that this method has better performance in noise removal, texture edge preservation and restoration.