We present density functionary theory (DFT) calculations on the structural parameters and electronic structure for iridium nitride by using the generalized gradient approximation (GGA) and the Perdew-Burke-Ernserhof (PBE) exchange-correlation functional. The lattice parameters and bulk modulus (B (0)) for the ground state are obtained, and the energy band structure and electron densities of states (DOS) of IrN2 are presented. It is found that IrN2 has a very close indirect energy gap. There is a strong covalent bond between the two nearest N atoms. This gives rise to a very high elastic modulus of IrN2 and reveals the quasimolecular nature of the N-2 in IrN2 crystal. Lattice parameters, bulk modulus, and the electronic structure of IrN2 under high pressure have also been investigated based on DFT. The compressibility along three cell vectors is very close to each other. The band gap increases a little with the pressure even when the pressure is up to 100 Gpa.