The electronic structure of the Ca/Si(111)-(3×2) surface has been investigated by angle-resolved photoelectron spectroscopy. Five surface states, none of which crosses the Fermi level, were observed in the bulk band gap, and one surface state was observed in a bulk band pocket. The dispersion features of three of the surface states in the band gap agree well with results from monovalent atom adsorbed Si(111)-(3×1) surfaces along the chain direction. The close resemblance indicates that the origins of the surface states are the same as or quite similar to those of the (3×1) surface. The two other states observed in the band gap have not been reported in the literature, and they are interpreted as surface states that occur on Ca/Si(111)-(3×2) due to the lower coverage (1/6 monolayer of Ca). Further, based on the finite surface state dispersion in the direction perpendicular to the Ca chains, we conclude that the electronic character of this surface is not completely one dimensional.