It focuses on an approach to generating 2D unstructured grids for the solution of Euler equations.Unlike the generation of unstructured grids before with background grids,the background information needed in Avancing Front Method is obtained directly with the distance to the airfoil surface.In solving the Euler equations,the cell centered finite volume method is used for space discretization,and four step Runge Kutta method is adopted for time marching.Two kinds of boundary condition are presented and three kinds of boundary conditions are applied and analyzed.The calculated results are given and discussed.