Markov random field models have extensively used in applications such as image segmentation and image restoration. In this paper, we consider the relation between the stationarity of parameters and the synthesized images for gauss-markov rnadom field which has the most popularly used among many MRF models. GMRF model, which is both wide-sense Markov and strict-sense markov, has AR representations and is also a kind of gibbs distribution. Therefore, we may approach in aspect of both AR models and gibbs models. We show the relation between the stationarity of parameters and the images which are synthesized by two approaching methods and derive the stationary regions of parameters in 1st order and isotropic 2nd order case.