This article introduces a novel probability distribution model, namely, complex isotropic $\alpha$ -Stable-Rician (CI $\alpha$ SR), for characterizing the data histogram of synthetic aperture radar (SAR) images. Having its foundation situated on the Lévy $\alpha$ -stable distribution suggested by a generalized central limit theorem, the model promises great potential in accurately capturing SAR image features of extreme heterogeneity. A novel parameter estimation method based on the generalization of method of moments to expectations of Bessel functions is devised to resolve the model in a relatively compact and computationally efficient manner. Experimental results based on both simulated and empirical SAR data exhibit the CI $\alpha$ SR model’s superior capacity in modeling scenes of a wide range of heterogeneity when compared with other state-of-the-art models as quantified by various performance metrics. Additional experiments are conducted utilizing large-swath SAR images, which encompass mixtures of several scenes to help interpret the CI $\alpha$ SR model parameters and to demonstrate the model’s potential application in segmentation and target detection.