The ground electronic state and the reasonable dissociation limit of SiH+ molecular ion have been correctly determined based on group theory and atomic and molecular reaction statics. The energy, equilibrium geometry and harmonic frequency of the ground electronic state of SiH+ molecular ion have been calculated using the method QCISD(T)/cc-pVQZ. The whole potential curves for the ground electronic state is further scanned using the above method, the potential energy functions and relevant spectroscopic constants of this state are then first obtained by least square fitting to the Murrell-Sorbie function (n=9) and the modified Murrell-Sorbie+c6 function, respectively. The present results showed that the calculated results based on the Murrell-Sorbie function (n=9) are in better agreement with the experimental values, with the relative errors between spectroscopic constants and the experimental values being 0.13%, 3.07%, 0.38%, 5.25% and 0.52% respectively. With the potential obtained at the QCISD(T)/cc-pVQZ level of theory, the total of 27 vibrational states are predicted when J=0 by numerically solving the radial Schrodinger equation of nuclear motion. The complete vibrational levels, inertial rotation and six centrifugal distortion constants are obtained for the ground electronic state of SiH+ molecular ion for the first time. Calculation results in the present work may provide theoretical supports for the further study of SiH+ molecular ion.