Consider a kind of generalized Nash equilibrium problems (GNEPs) whose objective functions are polynomials, and the constraints can be represented by polynomial equalities and inequalities. Gauss-Seidel typed Approach is one kind of natural easy implemented method to solve GNEP. We study some properties for this approach, and give out a computable criterion for Generalized Potential game (GPGs), the condition under which the convergence of this approach could be guaranteed.