The pressure dependence of the optical absorption edge of InN is investigated. Owing to the strong nonparabolicity of the energy bands, wurtzite InN exhibits enhanced optical absorption well above the absorption edge. The direct band gap of wurtzite InN increases linearly with pressure at 29±1 meV/GPa. The wurtzite-to-rocsksalt phase transition is observed at 15.3±0.5 GPa as a clear change in the absorption edge. We find that rocksalt InN is an indirect semiconductor with a band gap energy of around 1.0 eV. A higher energy direct transition is found at ∼2 eV. These results are discussed in terms of theoretical band-structure calculations.