Using accurate first-principles quantum calculations based on DFT (including the perturbation theory DFPT) with the range-separated hybrid HSE06 exchange-correlation functional, we predict essential fundamental properties (such as bandgap, optical absorption coefficient, dielectric constant, charge carrier effective masses and exciton binding energy) of two stable monoclinic vanadium oxynitride (VON) semiconductor crystals for solar energy conversion applications. In addition to the predicted band gaps in the optimal range for making single-junction solar cells, both polymorphs exhibit relatively high absorption efficiencies in the visible range, high dielectric constants, high charge carrier mobilities and much lower exciton binding energies than the thermal energy at room temperature. Moreover, their optical absorption, dielectric and exciton dissociation properties are found to be better than those obtained for semiconductors frequently utilized in photovoltaic devices like Si, CdTe and GaAs. These novel results offer a great opportunity for this stoichiometric VON material to be properly synthesized and considered as a new good candidate for photovoltaic applications.