Abstract: In this paper, we consider the discretization of generalized stationary Gaussian random fields. A sufficient and necessary condition for a generalized stationary Gaussian random field to be discretizable is given, and a sufficient condition for the large scale （or short scale） limit field of a generalized stationary Gaussian random field to be discretizable is obtained. Furthermore, a condition that a discrete stationary Gaussian field having a large scale limit can be imbeded in a discretizable generalized stationary Gaussian field having a large scale limit is obtained, too.