Based on first principles within density-functional theory, we establish three models of N doped anatase TiO2, Sm doped anatase TiO2 and Sm-N codoped anatase TiO2 by using the plane-wave ultrasoft pseudopotential method. We calculate their densities of states, band structures and absorption spectra. Their results show that although the N doped anatase TiO2 takes the best redshift, the Sm-N codoped anatase TiO2 makes better lifespan of electron and the Sm-N codoped anatase TiO2 is more stable.