Recent theoretical calculations and experimental results suggest that the strongly correlated material SmB6 may be a realization of a topological Kondo insulator. We have performed an angle-resolved photoemission spectroscopy study on SmB6 in order to elucidate elements of the electronic structure relevant to the possible occurrence of a topological Kondo insulator state. The obtained electronic structure in the whole three-dimensional momentum space reveals one electron-like 5d bulk band centered at the X point of the bulk Brillouin zone that is hybridized with strongly correlated f electrons, as well as the opening of a Kondo band gap (Delta(B) similar to 20 meV) at low temperature. In addition, we observe electron-like bands forming three Fermi surfaces at the center Gamma point and boundary (X) over bar point of the surface Brillouin zone. These bands are not expected from calculations of the bulk electronic structure, and their observed dispersion characteristics are consistent with surface states. Our results suggest that the unusual low-temperature transport behavior of SmB6 is likely to be related to the pronounced surface states sitting inside the band hybridization gap and/or the presence of a topological Kondo insulating state.