The nature of the band gap of indium oxide is still a matter of debate. Based on optical measurements the presence of an indirect band gap has been suggested, which is 0.9 to 1.1 eV smaller than the direct band gap at the Γ point. This could be caused by strong mixing of O 2p and In 4d orbitals off Γ. We have performed extensive density functional theory calculations using the LDA+U and the GGA+U methods to elucidate the contribution of the In 4d states and the effect of spin-orbit coupling on the valence band structure. Although an indirect band gap is obtained, the energy difference between the overall valence band maximum and the highest occupied level at the Γ point is less than 50 meV. It is concluded that the experimental observation cannot be related to the electronic structure of the defect free bulk material.