A parameter estimator of the heavy-tailed Rayleigh prior model was proposed for the multi-look averaged amplitude Synthetic Aperture Radar (SAR) image. First, the multiplicative model of SAR image was changed into the additive one according to the logarithmic transformation. Then, the expectation and variance of the log-transformed original image were derived using the theory of negative-order moments. Lastly, the expectation and variance of the log-transformed speckle were obtained based on the Gaussian approximation of the log-transformed speckle. The proposed estimator is easy to be implemented in the form of analytical expressions. Parameter estimation experiments on Monte Carlo simulations and real SAR images demonstrate that the proposed estimator can efficiently estimate the parameters of the heavy-tailed Rayleigh prior model from the multi-look averaged amplitude SAR image.