The potential energy has been calculated for the 42 lowest electronic states of symmetries Omega=12,32,52, for the molecular ion RbH(+). Using an ab initio method, the calculation is based on nonempirical pseudopotentials and parametrized [script-l]-dependent polarization potentials. Gaussian basis sets have been used for both atoms, and spin-orbit effects have been taken into account. The spectroscopic constants for 19 electronic states have been calculated by fitting the calculated energy values to a polynomial in terms of the internuclear distance r. The permanent dipole moment and the transition dipole moments have been calculated for the considered Omega states. Through the canonical functions approach the eigenvalue E(v), the abscissas of the corresponding turning points (r(min) and r(max)) and the rotational constants B(v) have been calculated. The comparison of the present results with those available in literature shows a very good agreement.