An adiabatic study of 1-34 (1,3)Sigma(+) electronic states of barium hydride ion (BaH+) is presented for all states dissociating below the ionic limit Ba2+H-. The 1-20 (1,3)Pi and 1-12 (1,3)Delta states have been also investigated. In our approach, the valence electrons of the Ba2+ ion described by an effective core potential (ECP) and core polarization potential (CPP) with l-dependent cutoff functions have been used. The ionic molecule BaH+ has been treated as a two-electron system, and the full valence configuration interaction (CI) is easily achieved. The spectroscopic constants R-e, D-e, T-e, omega(e), omega(e)x(e), and B-e are derived. In addition, vibrational level spacing and permanent and transition dipole moments are determined and analyzed. Unusual potential shapes are found and also accidental quasidegeneracy in the vibrational spacing progression for various excited states. The (1)Sigma(+) states exhibit ionic charge transfer avoided crossings series which could lead to neutralization or even H- formation in collisions of H+ with Ba.