We have employed first-principles calculations of density functional theory (DFT) with GGA and GGA+U exchange correlation to study structural, magnetic, and electronic properties of chromium nitride (CrN) in the rock salt (NaCl) structures. The obtained data from DFT calculations is used as an input in high-temperature series expansions (HTSEs) combined with the Pade approximants (PA) method and Monte Carlo simulation (MC) for the Ising model to investigate the magnetic properties of CrN. The obtained results show that CrN is more stable in the antiferromagnetic order, and undergoes structural and magnetic transitions from an antiferromagnetic NaCl structure to a nonmagnetic Pnma phase at 201 GPa. The density of states (DOS) with GGA approach shows that CrN has a metallic behavior in both FM and AFM configurations whereas with GGA+U CrN is semiconductor in AFM and half-metallic in FM order. The Neel temperature (TN) obtained by HTSE and MC is in agreement with available experimental data.