Chang et al. anticipated the portion mechanical characteristics of tetragonal structure Zr2CN (P4/mmm, Ceram. Int., 46 (2020) 1124), however, the results deviated greatly from the experimental values. Herein, the elastic, hardness, fracture toughness, and partial thermodynamic characteristics of t-Zr2CN are reinvestigated through the first-principles calculations. The ground states lattice parameters are found to agree well with the available theoretical result. The Zr2CN is found to be both thermodynamically and mechanically stable at the ground state according to the formation enthalpy and single-crystalline elastic constants. The polycrystalline moduli can be estimated through the single-crystalline elastic constants. The result demonstrates that Zr2CN is elastic anisotropy, brittle, poorly machinable, and has a high Vicker hardness (20.9 GPa). Finally, the high Debye temperatures (706.8 K), and melting temperature (2472 K) make it suitable for use as a thermal barrier material.