The structural, elastic, electronic and thermodynamic properties of PtN2 have been studied in fluorite (C1), pyrite (C2), marcasite (C18), CoSb2, simple hexagonal (denoted SH hereafter), simple tetragonal (denoted ST hereafter) and Layer structure (hereafter denoted as LS) phase by performing ab initio calculations within the generalized gradient approximation (GGA). The equilibrium lattice parameters, bulk modulus and its pressure derivative are in agreement with the available theoretical results and experimental data. The most stable structure is C2 phase through calculating the enthalpy, while the others are metastable. It is noted that no phase transition occurs between difference phases in the pressure range studied here. The density of states indicates that C2-PtN2 is semiconductor with a band gap of 1.5 eV. The Young's modulus, Poisson's ratio and anisotropy factor have been predicted. We note that the elastic constant, bulk modulus, shear modulus, compressional and shear wave velocity increase monotonically with increasing pressure. The Debye temperature, thermal expansion and heat capacity increase with pressure.