The molecular chemical structure of poly(methyl methacrylate) (PMMA) surface has been Studied by sum frequency generation (SFG) vibrational spectroscopy. By using various methods, we have shown that reflected SFG spectra of PMMA collected in our experiments only come from the polymer/air interface, not from the polymer/substrate or the bulk polymer. These SFG spectra are dominated by the vibrational bands from the ester methyl group. Ranges of orientation and orientation distribution of the ester methyl group on the PMMA surface have been deduced. The antisymmetric stretching vibrational band of the alpha methyl group has been detected on the PMMA surface. Analysis shows that the alpha methyl groups are lying down on the surface. The methylene group has not been observed in SFG spectra, For comparison, we have also studied surface chemical structures of poly(methyl acrylate) (PMA) and dimethyl succinate by SFG.