Electrical conducting properties of DNA duplexes sandwiched between Au electrodes have been investigated by use of first-principles molecular simulation based on DFT and Green's function to elucidate the origin of their base sequence dependence. The theoretically simulated effects of DNA base sequence on the electrical conducting properties are in qualitative agreement with experiment. The HOMOs localized on Guanine bases have the major contribution to the electrical conductivity through DNA duplexes.