The charge densities, band structure, density of states, dielectric functions of Si-doped [Formula: see text]-Ga 2 O 3 have been investigated based on the density functional theory (DFT) within the hybrid functional HSE06. The heavy doping makes conduction band split out more bands and further influences the band structure. It decreases the band gap and changes from a direct gap to an indirect gap. After doping, the top of the valence bands is mainly composed by the O-2p states, Si-3p states and Ga-4p states and the bottom of the conduction bands is almost formed by the Si-3s, Si-3p and Ga-4s orbits. The anisotropic optical properties have been investigated by means of the complex dielectric function. After the heavy Si doping, the position of absorption band edges did not change much. The slope of the absorption curve descends and indicates that the absorption became more slow for Si-doped [Formula: see text]-Ga 2 O 3 than undoped one due to the indirect gap of Si-doped [Formula: see text]-Ga 2 O 3 .