We have performed combined angle-resolved photoemission spectroscopy (ARPES) experiments and density functional theory (DFT) calculations of the electronic structure of the Ir(111) surface, with the focus on the existence of energy band gaps. The investigation was motivated by the experimental results suggesting Ir(111) as an ideal support for the growth of weakly bonded graphene. Therefore, our prime interest was electronic structure around the [Formula: see text] symmetry point. In accordance with DFT calculations, ARPES has shown a wide energy band gap with the shape of a parallelogram centred around the [Formula: see text] point. Within the gap three surface states were identified; one just below the Fermi level and two spin-orbit split surface states at the bottom of the gap.