The structures, electronic properties, elasticity, theoretic hardness, and Debye temperatures of chromium carbides, Cr3C2, Cr7C3 and Cr23C6 were calculated by the density functional theory of first-principles. The results show that the deviation of equilibrium lattice parameters from the experimental data is small. The bond in these compounds is the mixture of covalent, ionic and metallic bonding. The most stable phase belongs to Cr3C2; the values of theoretic hardness of Cr3C2, Cr7C3 and Cr23C6 are 20.9, 18.3 and 13.2 GPa, respectively, which are in good agreement with recent experimental results. Besides, the Debye temperatures of chromium carbides were predicted.