The band gap reductions, dielectric functions and absorption coefficients of the Ga1−xZnxN1−xOx and In1−xZnxN1−xOx (x = 0.00, 0.25, 0.50, 0.75, and 1.00) alloys were calculated, employing the partial self-consistent GW approximation. As a comparison, the local density approximation (LDA) and the Heyd–Scueria–Ernzerhof (HSE) hybrid functional were also used to calculate the gap reduction. Both Ga1−xZnxN1−xOx and In1−xZnxN1−xOx alloys show strong band gap bowing. As a result, the band gap energy in Ga1−xZnxN1−xOx is reduced by Eg(GaN) − Eg (Ga1−xZnxN1−xOx) = 1.61, 2.01 and 1.91 eV for x = 0.25, 0.50, and 0.75, respectively. This allows optoelectronic devices based on GaN and ZnO with more efficient absorption or emission of light in the visible light range. The calculated dielectric functions and absorption spectra demonstrate that the band gap reduction enhances the optical absorption around the 2.5 eV region. Interestingly, the In1−xZnxN1−xOx alloy with x = 0.25 has the large optical absorption coefficient in the energy region 0.69–6.0 eV, and the alloy has very good absorption at 2–3 eV.