In this paper, we introduce a novel mixture model of the SAR amplitude image, which is proposed as an approximation to the heavy-tailed Rayleigh model. The limitation of the heavy-tailed Rayleigh model in SAR image application is discussed. We also present an expectation-maximization (EM) algorithm based parameter estimation method for the Cauchy-Rayleigh mixture. We test the new model on some simulated data in order to confirm that is appropriate to the heavy-tailed Rayleigh model. The performance is evaluated by some statistic values (cumulative square errors (CSE) < 0.013, correlation coefficient (CC) > 0.99 and Kolmogorov-Smirnov distance (K-S) < 0.03). Finally, the performance of the proposed mixture model is tested on some real SAR images and compared with other models, including the heavy-tailed Rayleigh and Nakagami mixture models. The result indicates that the proposed model can be an optional statistical model for amplitude SAR images.