The structure and performance relationship has attracted a great many of attentions. The electronic structure and mechanical properties of the quaternary high-entropy carbide ceramic (Hf_0.25Zr_0.25Ta_0.25Nb_0.25)C and binary metal carbide systems AC(A = Hf, Zr, Ta and Nb) are studied by density functional theory calculations. By analyzing the thermodynamic properties of high-entropy compounds, it is known that (Hf_0.25Zr_0.25Ta_0.25Nb_0.25)C can form a single-phase solid solution. It can be obtained from the mechanical performance parameters that the calculated parameters roughly obey the rule of mixture, the Vickers hardness of (Hf_0.25Zr_0.25Ta_0.25Nb_0.25)C is greater than the average value of the four binary carbides that compose it; the Poisson's ratio ν and G/B value of (Hf_0.25Zr_0.25Ta_0.25Nb_0.25)C show that it is a brittle material, similar to constituent binary carbides. By analyzing their electronic structure, it was found that they are all conductors. The quaternary high-entropy carbides (Hf_0.25Zr_0.25Ta_0.25Nb_0.25)C shows an increase in conductivity, its existence covalent bonds are mainly composed of the orbital hybridization formation of C-p and A-d (A = Hf, Zr, Ta and Nb), due to the heterogeneity of coexisting chemical bonds in carbides, the mechanical properties of the material is further improved.