The exploration of topological Dirac semimetals with intrinsic superconductivity can be a most plausible way to discover topological superconductors.We propose that type-Ⅱ Dirac semimetal states exist in the band structure of TaC,a well-known s-wave superconductor,by using the first-principles calculations and the k.p effective model.The tilted gapless Dirac cones,which are composed of Tad and C p orbitals and are protected by C4v symmetry,are found to be below the Fermi level.The bands from Tad orbitals are greatly coupled with the acoustic modes around the zone boundary,indicating their significant contribution to the superconductivity.The relatively high transition temperature ～10.5 K is estimated to be consistent with the experimental data.To bring the type-Ⅱ Dirac points close to chemical potential,hole doping is needed.This seems to decrease the transition temperature a lot,making the realization of topological superconductivity impossible.