Information on the energy band gaps, the lattice parameters and the lattice matching to available substrates is a prerequisite for many practical applications. A pseudopotential formalism within the virtual crystal approximation is used to the zinc-blende AlxGayIn1-x-yN quaternary alloys lattice matched to GaN substrate to predict their energy band gaps and optical properties. The range of compositions for which the alloy is lattice-matched to GaN is determined. Very good agreement is obtained between the calculated values and the available experimental data. The compositional dependence of direct and indirect band gaps and dielectric constants has been investigated. The information derived from this study may be useful for ultraviolet optoelectronic applications. (C) 2008 Elsevier B.V. All rights reserved.