The energy band structures, density of states and optical properties of Mg2Si and Ag , Al-doped Mg2Si have been calculated systemically by first-principles pseudopotential method based on density functional theory (DFT). The calculated results show that Mg2Si is an indirect semiconductor with the band gap of 0.2994 eV, the valence bands of Mg2Si are composed of Si 3p, Mg 3s, 3p, the conduction bands are mainly composed of Mg 3s, 3p as well as Si 3p, the static dielectric function is 18.89, and the refractive index is 4.3460. Ag-doped Mg2Si sample is p-type, the valence bands are composed of Si 3p, Mg 3s, 3p and Ag 3p, 4d and 5s, static dielectric function is 11.01, and the refractive index is 3.3175 after doping Ag. Al-doped Mg2Si sample is n-type, the conduction bands are composed of Mg 3s, 3p, Si 3p, and Al 3p, the static dielectric function is 87.03, and the refractive index is 9.3289 after doping Al. The electronic structure of Mg2Si can be modulated effectively by doping. The results offer theoretical data for the design and application of optoelectronic materials of Mg2Si.