We employ ab initio plane-wave pseudopotential density functional theory to calculate the coordinates， equilibrium lattice parameters，bulk modulus，shear modulus and elastic constant of PtN2，and those calculated results agree well with the other experimental data and the published theoretical data. The curve of volume dependence of energy indicates the energy of STAAstructure is lower than that of pyrite structure. According to our result and the experimental criterion raised by Pugh, we come to the conclusion that the PtN2 is a very hard and fragile material. But when the pressure increases, the PtN2 becomes malleable gradually. It is revealed that the pyrite structure of the PtN2 is a semiconductor and the STAA structure of the PtN2 is a conductor by analyzing their density of states and band structure.