Conduction band edge (CBE) and valence band edge (VBE) positions of InxGa1-xN photoelectrodes were computed using density functional theory methods. The band edges of fully solvated GaN and InN model systems were aligned with respect to the standard hydrogen electrode using a molecular dynamics hydrogen electrode scheme applied earlier to TiO2/water interfaces. Similar to the findings for TiO2, we found that the Purdew-Burke-Ernzerhof (PBE) functional gives a VBE potential which is too negative by 1 V. This cathodic bias is largely corrected by application of the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional containing a fraction of Hartree-Fock exchange. The effect of a change of composition was investigated using simplified model systems consisting of vacuum slabs covered on both sides by one monolayer of H2O. The CBE was found to vary linearly with In content. The VBE, in comparison, is much less sensitive to composition. The data show that the band edges straddle the hydrogen and oxygen evolution potentials for In fractions less than 47%. The band gap was found to exceed 2 eV for an In fraction less than 54%.