A detailed [C2H2NS+] potential energy surface in singlet, including 45 minimum isomers and 57 transition states, is built up at the B3LYP/6-311G(d,p) and CCSD(T)/6-311G(2df,p) (single-point) levels in order to explore the mechanisms of the important ion-molecule reactions between CCN+/CNC+ and H2S. For the reactions of both CCN+ and CNC+ toward H2S, product HCS+ + HNC may be the most abundant followed by the much less HCNH+ + CS and then HCS+ + HCN. Significant discrepancies on the product distributions are found between our calculated results and previous experimental finding. On the other hand, the reaction of HCNH+ + CS to form HCS+ + HCN/HNC is also considered by the [C2H2NS+] PES. For such reaction, the barrierless association may lead to the adduct HNC(H)CS+, while the proton-transfer may barrierlessly lead to product HCS+ + HCN/HNC via the hydrogen-bound complexes SCH...NCH+/SCH...CNH+. The computations reported in this paper may represent the first theoretical study on the chemical reactivity of the C2N+ ion and may thus provide a useful guide for understanding the mechanisms of the other analogous reactions such as those of C2N+ with H2O, CH4, NH3, CH3OH, etc. The present calculations may also provide useful information for future laboratory investigations on the HCNH+ + CS reactions that have not been previously studied. Interstellar implications of the title reactions are discussed.