In this letter, a novel maximum a posteriori (MAP) filter for synthetic aperture radar (SAR) images is developed. We characterize the return signal of SAR using the Cauchy-Rayleigh mixture model, which is an approximation to the heavy-tailed Rayleigh distribution. The parameters of the Cauchy-Rayleigh mixture model are estimated from the noisy observation by using the expectation-maximization algorithm. Finally, we compare the proposed filter with several classical spatial filtering techniques by applying them on simulated data and various real SAR images. Experimental results show that the Cauchy-Rayleigh-mixture-based MAP filter performs better for speckle removal than the other methods, including Lee, Kuan, and Γ-MAP.