The global potential energy surface (PES) of HCS+(X1Σ+) is constructed using many-body expansion (MBE) methodology. The obtained analytical function is found by fitting the 7907 ab initio energy points computed at the Davidson-corrected multi-reference configuration interaction level with the aug-cc-pV(5+d)Z basis set. The final root mean square error is 0.0419 eV, and the maximum deviation is 0.2039 eV, showing that the analytical formula agrees well with the energy points. The topological features are calculated and discussed based upon the analytical PES of HCS+(X1Σ+). The reaction probability, integral cross sections and other details of the C+(2P) + SH(X2Π) → H(2S) + CS+(X2Σ+) reaction are investigated using the quasi-classical trajectory and time-dependent quantum wave packet methods.