Abstract In spite of the proved usefulness ab initio investigation analyzing optoelectronic properties in the dilute-nitride zinc blende (InxGa1−xNyAs1−y/GaAs) alloys. First principles calculations in the framework of the Full-Potential LAPW scheme have been carried out. The dilute-nitride zinc blende (InxGa1−xNyAs1−y) was modeled at selected nitrogen compositions of y=3.125, 6.25 and 9.375 percent lattice matched to GaAs. We pay attention to the InxGa1−xNyAs1−y alloy which can be perfectly lattice matched to the GaAs over its entire compositional range. In our study, this is achieved when a condition y~2.7x is maintained. The band structure calculations were performed with and without relaxation by using the generalized gradient approximation of Engel and Vosko (EV-GGA) as well as by the modified Becke-Johnson potential exchange (TB-mBJ). The action of the localized potential of subsisted nitrogen atoms was attributed to effect of relaxation. Increasing both indium and nitrogen compositions leads to decreasing energy band gap. In addition, a band anti-crossing model (BAC) was also adopted to study the composition dependence of the direct band gap of quaternary alloys, building a bridge between their electronic and linear optical properties.