In this wok, we present the density functional theory (DFT) calculations of cubic III-N based semiconductors by using the full potential linear augmented plane-wave method plus local orbitals as implemented in the WIEN2k code. Our aim is to predict the pressure effect on structural and electronic properties of III-N binaries and ternaries. Results are given for structural properties (e.g., lattice constant, elastic constants, bulk modulus, and its pressure derivative) and electronic properties (e.g., band structure, density of states, band gaps and band widths) of GaAs, GaN, AlN, and InN binaries and GaAsN ternaries. The proposed model uses GGA exchange-correlation potential to determine band gaps of semiconductors at Gamma, L and X high symmetry points of Brillouin zone. The results are found in good agreement with available experimental data for structural and electronic properties of these semiconductors.