Image denoising is a fundamental problem in image processing. Images may be contaminated by different kinds of noises in different imaging applications. Cauchy noise often arises in many practical applications, such as radar and sonar image processing. We consider removing Cauchy noise in the images. We develop a generalized low-rank model for Cauchy noise removal and design a proximal alternating algorithm to solve this nonconvex model. The convergence of the algorithm is also demonstrated. Numerical experiments illustrate that the proposed method can remove Cauchy noise in the images much better than the existing state-of-the-art methods in terms of both image recovered visual qualities and measure quantities.