A new class of noiseproof adaptive Bandelet bases (NA-Bandelet bases) is proposed. First, by employing soft-threshold function and the threshold obtained by SURE principle, the approximation of the original image in each dyadic square is computed, and then the geometrical direction in each dyadic square is found out according to the principle of the minimal approximation error. Secondly, the small dyadic square is combined based on the principle of Minimum Mean Square Error (MMSE), so the directions of NA-Bandelet bases are determined at last. Therefore, a novel denoising method based on the NA-Bandelet bases is presented, and it is applied to denoise and despeckle the optical image and SAR image respectively. Compared with the denoising methods based on Orthonormal wavelet bases and Bandelet bases, the experiment result shows that the algorithm proposed in the paper can reduce noise more effectively with improved edge-preserving ability.