Aiming at the defects of existing infrared image denoising algorithms in edge restoration and preservation, an infrared image denoising method based on complex wavelet and maximum a posteriori estimation is proposed. This method takes full advantage of the excellent characteristics of dual tree complex wavelet transform, such as multi-resolution analysis, translation invariance and multi-directional selectivity, performs dual tree complex wavelet transformation for noisy infrared image; and based on the assumption of probability density distribution of Gaussian noise and noiseless image, the maximum a posteriori estimation of wavelet coefficients of noiseless image is made in the wavelet domain to realize the denoising and restoration of infrared images. Infrared image denoising experiments have proven the effectiveness of the proposed method, this method not only removes noise effectively, but also maintains and recovers the edge details perfectly, the image quality indexes PSNR and SSIM of denoising are 1dB more and 2% higher than the existing methods, respectively.