The preparation of TiC coating on Ti alloy surface to improve the wear resistance has attracted attention from researchers in aerospace field. The service life of TiC coating is related to the interfacial adhesion properties between TiC coating and Ti alloy substrate. However, it is difficult to explain its interfacial adhesion mechanism by experimental methods. Based on the termination of atoms on the TiC surface, two TiC/Ti interface models named as the C-terminated-TiC(111)/Ti(0001) and Ti-terminated-TiC(111)/Ti(0001) interface were constructed by first-principles. The interfacial electronic characteristic of C—Ti bond is a mixture of polar covalent and metal bonds, and that of Ti—Ti bond is the metal bond. The tensile strains of both C-terminated-TiC(111)/Ti(0001) and Ti-terminated-TiC(111)/Ti(0001) interface in the fracture stage are ranged from 12% to 14%. Their maximum tensile stresses are 16.201 GPa and 15.590 GPa, respectively. The sliding potential energy surface maximum of C-terminated-TiC(111)/Ti(0001) and Ti-terminated-TiC(111)/Ti(0001) interface are 5.387 J/m² and 0.271 J/m², respectively. And the sliding potential barriers on the minimum energy path are 2.094 J/m² and 0.136 J/m² with an ideal shear strength of 20.32 GPa and 1.61 GPa, respectively. In summary, the interfacial adhesion property of C-terminated-TiC(111)/Ti(0001) interface is better than that of Ti-terminated-TiC(111)/Ti(0001) interface.