The band structure, total density of states and partial density of states of pure and In-doped wurtzite ZnO have been investigated by using the first-principles ultrasoft pseudo potential approach of the plane wave. The calculation indicates that the band gap of ZnO is reduced by In doping. The energies of both the conduction band minimum and the valence band maximum decrease with increasing In-doping concentration, but the decrease of the conduction band minimum is much more pronounced than that of the valence band maximum, which leads to narrowing of the band gap. Moreover, it was found that In-doping can cause increase of the lattice constant, which also reduces the band gap.