The relation among grain edge length, grain size and topology is studied by large-scale Potts model-Monte Carlo simulation. The results show that the grain edge length is related to the number of grain faces by a linear relation, which is also observed to hold in Poisson-Voronoi structure and average N-hedra. The distribution of the grain edge lengths maintains self-similarity in the period of quasi-stationary grain growth. The average length of an edge segment in individual grains varies with grain size （or the number of grain faces）,thereby indicating that assuming the lengths of edge segments in all individual grains to be equal averagely as does in some models is subject to some limitations. The data of Monte Carlo simulated grains and pure iron show that the grain size is related to the face number by a curve convex upward.