Materials with superconductivity and a nontrivial band structure near the Fermi level are promising candidates in realizing topological superconductivity. Using first-principles calculations, we systematically investigated the stability, mechanical properties, superconductivity, electronic structures, and topological states of hexagonal TaC and NbC. The results show that they are stable and have excellent mechanical properties. We predicted that these two carbides are strong electron-phonon coupling superconductors with superconducting transition temperatures of 14.8 and 17.1 K, respectively. Strong coupling is mainly dominated by in-plane Ta/Nb atomic vibrations and in-plane Ta/Nb-dxy/dx2-y2 electronic orbitals. The electronic structure calculations demonstrate that a nodal line and a triply degenerate point coexist when not including the spin-orbit coupling (SOC) effect. After including the SOC effect, the nodal line is gapped. The complicated surface states are also calculated and need further experiments to verify. The present results indicate that the hexagonal TaC and NbC are potential candidates as topological superconductors, and pave the way towards exploring the superconductivity and topological materials in condensed matter systems.