An aerial image simulator for the synchroton X-ray proximity lithography system has been developed. The modal expansion method and Rayleigh-Sommerfeld diffraction theory are used in calculating the aerial image which is formed by diffracting of the partially coherent X-ray, Experimental results of PALC(POSTECH Advanced Lithography Center) lighography system and simulated results are compared. The experimental and theoretical values of the width of replicated lines are consisted with the relative error less than ~5%. The method to determine the divergent angle of X-ray from the analysis of the width of replicated lines is given.