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In this letter, a new method for denoising remote-sensing images based on partial differential equations (PDEs) is proposed. The method employs the similarity between the different band images in a multicomponent image. Initially, one of the noise-free images in multicomponent remote-sensing images as a prior is introduced into the PDE denoising method. To make use of the priors of the noise-free image in denoising, we construct a new smoothing term for the PDE so as to compute the total variation. The new smoothing term refers to a specific smoothing direction and a specific smoothing intensity of the reference image when denoising the noisy image. The proposed smoothing term is added as a new constraint into the PDE denoising method. Based on the proposed method, the similarity of the directions of the edges between the noisy image and the reference image enables the new algorithm to smooth out more noise and conserve more detail in the denoising process. We also present the discrete form of the proposed denoising model. Multispectral remote-sensing images and hyperspectral remote-sensing images are experimented in this letter. A better performance is achieved by the proposed method when compared with other methods.