In this study, for the concentrations of x=0.0, 0.25, 0.5, 0.75 and 1.0, the calculations of the physical properties of GaP$_{1–x}$N$_x$ mixed alloys are presented. To perform these calculations, we employ WIEN2k computational code based on the approach of full-potential linearized augmented plane wave plus local orbital FP(L(APW+lo)), which is framed within density functional theory. At first, at the level of the WC-GGA scheme, the phase stability of the GaP$_{1–x}$N$_x$ alloys in their sodium chloride (B1), zinc-blende (B3) and wurtzite (B4) structures were analysed. The analysis of our results shows that GaP, GaP$_{0.75}$N$_{0.25}$, GaP$_{0.5}$N$_{0.5}$ and GaP$_{0.25}$N$_{0.75}$ are stable in B3 crystal structure, whereas GaN is found to be stabilized in wurtzite structure. Moreover, for each concentration, the pressure-induced phase transition of B3 and B4 structures to B1 structure is also explored. On the other hand, the calculations of the band structures show changeover of indirect band gap energy for GaP with energy gap 2.23 eV to direct band nature for GaN with band gap energy 3.183 eV. Likewise, the optical properties are explored for the energy range of 0.0–40 eV. The investigations of the thermodynamic properties, for example, entropy, Debye temperature, specific heat are carried out at the level of the ‘quasi-harmonic Debye model’. Moreover, the effect on the thermodynamic properties by temperature and pressure is also predicted. The results obtained for band gap energy as well as the optical absorption coefficients endorse that the investigated compositions of the alloys are very right for infrared to visible region optoelectronic applications.