The potential energy curves (PECs) for ground state (X1+) and five low-lying electronic states (11-, 11, A1, 15+, 25+) of the GeS molecule have been studied by multi-reference configuration interaction (MRCI) plus Davidson correction (+Q) with all-electron basis set aug-cc-pv5Z. Results show that the 25+ state is an unstable repulsive state, and the others are bound states, and the six electronic states are dissociated along the same channel, Ge(3P)+S(3P). The adiabatic transition energy Te equilibrium bond length Re, dissociation energy De, harmonic frequency e, anharmonic constant exe, and equilibrium dipole moments are obtained by fitting the PECs for the X1+, 11-, 11, A1 and 15+ states. While Re is 2.034 , De 5.728 eV, e 571.73 cm-1, exe 1.6816 cm-1, the equilibrium dipole moment is 1.9593 Debye for the ground state. The values of Te are 25904.81, 26209.22, 32601.19, 43770.26 cm-1 for 11, 11, A1 and 15+ states, respectively; the values of Re are 2.313, 2.322, 2.188, 2.8790 for 11, 11, A1 and 15+ states, respectively; the values of De are 2.524, 2.487, 1.694, 0.3036 eV for 11-, 11, A1 and 15+ states, respectively; the values of e are 358.90, 353.08, 376.32, 134.96 cm-1 for 11-, 11, A1 and 15+ states, respectively; the values of exe are 1.2421, 1.2151, 1.6608, 1.9095 cm-1 for 11, 11, A1 and 15+ states, respectively, and the values of equilibrium dipole moments are 1.3178, 1.4719, 1.5917, -1.9785 Debye for 11-, 11, A1 and 15+ states, respectively. By solving the radial Schrdinger equation of nuclear motion, the 30 vibration levels and 30 inertial rotation constants (J=0) for X1+, 11-, 11, A1 and 15+ states are also obtained, and all of are in good agreement with the available experimental and other theoretical values.