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In this work, adiabatic potential energy curves, spectroscopic constants, dipole moments, and vibrational levels for numerous electronic states of magnesium hydride molecular ion (MgH(+)) are computed. These properties are determined by the use of an ab initio method involving a nonempirical pseudopotential for the magnesium core (Mg), the core polarization potential (CPP), the l-dependent cutoff functions and the full valence configuration interaction (FCI). The molecular ion is thus treated as a two-electron system. Our calculations on the MgH(+) molecular ion extend previous theoretical works to numerous electronic excited states in the various symmetries. A good agreement with the available theoretical and experimental works is obtained for the spectroscopic constants, the adiabatic potential energy curves, and the dipole moments for the lowest states of MgH(+).