Binary chromium carbides display excellent wear resistance, extreme stiffness and oxidation resistance under high temperature. The influence of applied pressure on electronic structure, elastic behavior, Debye temperature and hardness of Cr7C3, Cr3C2 and Cr23C6 have been investigated by the density functional theory (DFT) method. The results reveal that lattice parameters and formation enthalpy display an inverse relationship with applied pressure, and Cr3C2 exhibited optimal structural stability. Moreover, Cr-C orbital hybridization tends to be stronger due to the decreased partial density of states (PDOS) of the Cr atom. The difference in electronic distribution of binary carbides has also been investigated, which confirmed that overall orbital hybridization and covalent characteristics has been enhanced. The theoretical hardness was elevated according to the higher bond strength and bond density. In accordance with structural stability data, Cr3C2 has shown maximum theoretical hardness. Furthermore, the anisotropic nature of hardness has been evaluated with external pressure. Cr3C2, and the highest isotropic hardness behavior along with an increase in hardness values with increasing pressure has been observed. In addition, the variation in Debye temperatures of binary chromium carbides under applied pressure has also been predicted. The results provide a theoretical insight into electronic, mechanical and thermodynamic behavior of three binary chromium carbides and show the potential of these novel carbides in a wide range of applications.