In this paper, we have studied the structural, electronic, magnetic, elastic and thermodynamic properties of the cubic perovskite system Cr4N using the first-principles calculations based on density functional theory (DFT) with the generalized gradient approximation (GGA). Our results show that the Cr4N is more stable in a ferrimagnetic configuration (FIM) and in a ferromagnetic arrangement (FM), Cr4N is nonmagnetic compound (NM). Density of States (DOS) and band structure calculations show a metallic behavior of Cr4N. The calculated elastic constants satisfy the Born mechanical stability criterion. Based on the calculated data of Poisson’s ratio, Cr4N have ionic bonding. According to the B/G values, the compound under investigation is found to be brittle nature in FIM configuration and ductile nature in FM and NM configurations. The exchange interactions of Cr4N, were calculated to obtain the critical temperature (TC) from Monte Carlo calculations. The obtained value of TC (295 K) is in good agreement with other theoretical works.