In order to enrich the information of the electronic ground states and excited states of hydrogen persulfide molecule HSSH and hydrogen persulfide monovalent cation HSSH+ the B3LYP calculation of density functional theory with the 6-311++g(3df,3pd)basis set level was used to investigate them. The equilibrium configurations, spectroscopic constants, total energies and zero point vibration energies of HSSH in the ground state and HSSH+ in the ground state and excited states are obtained. The studies show that HSSH is a long symmetric gyroscope molecule with C2 symmetry and the dihedral angle is 90.66°, whereas HSSH+ has two stable isomers, cis-HSSH+ (the dihedral angle 0°) and trans-HSSH+(the dihedral angle 180°). This work also shows that the electron energy of the trans-HSSH+ isomer is 0.129 eV lower than that of the cis-HSSH+ isomer . In addition, the ground-state and excited state electronic structures of HSSH+ have also been calculated.