Studies properties of Szasz-Mirakjan operators, such as maintain shape approximation and consistent convergence. Obtains the approximation order of Szasz-Mirakjan operators with weighted moduli of smoothness on the basis of V. Totik′s approximation theory and gets the approximation order of Szasz-Mirakjan operators with general moduli of smoothness from Devore-Freud′s approximation theory.