A global potential energy surface (PES) representation of the C(P-3) + SH(X (2)Pi) -> H(S-2) + CS(a (3)Pi) system is developed by fitting plenty of precise energies obtained through the ab initio calculation with aug-cc-pVQZ and aug-cc-pV5Z basis sets via extrapolation to the complete basis set limit. The topographical characteristics of the PES are examined in detail, and it is found that they agree well with previous calculations available in the literature. By utilizing the PES of HCS(A(2)A ''), the corresponding reaction is investigated using the quasi-classical trajectory (QCT) method in the collision energy range of 0.08-1.0 eV. The minimum energy paths (MEPs) calculated on the basis of the present PES indicate that the C(P-3) + SH(X (2)Pi) -> H(S-2) + CS(a (3)Pi) reaction is exothermic, with the exothermicity similar to 0.204 eV. The calculation for the capture time indicates that the reaction is mainly governed by the indirect mechanism at the lower collision energy, while, for higher collision energy, the direct mechanism is in coexistence with the indirect mechanism, and the latter one plays a dominant role.