SAR technology has been intensively implemented for geo-sensing and mapping purposes due to its advantages of high azimuthal resolution and weather-independent operation compared to other remote sensing technologies. Modelling SAR image data consequently becomes a prominent topic of interest, especially for data populations with impulsive signal features, which are common in SAR images of urban areas. A recently proposed model named Cauchy-Rician has manifested great potential in modelling extremely heterogeneous SAR images, yet the work only provided a MCMC-based parameter estimator that demands considerable computational power. In this work, a novel analytical parameter estimation method based on algebraic moments is proposed to provide stable and accurate estimation of the parameters of the Cauchy-Rician model with significant improvement on computation speed.