(Symmetric alpha-Stable) model is an accurate image model in Wavelet-domain. But this method needs lots of computation. In this paper, a new model, Gaussian-Cauchy model, was proposed on the base of model. Using this model characterizing the real-world images prior model can reduce computations obviously. In addition, the logarithm transform changes its statistical characteristic, so we must adjust the mean in the process. Experimental results show that there is almost nothing differences between this model and model in edges、 SNR (signal to noise ratio) and subjective visual effect.