  We investigate the superconductivity in Sr$_2$RuO$_4$ on the basis of the
three-dimensional three-band Hubbard model. We propose a model with Coulomb
interactions among the electrons on the nearest-neighbor Ru sites. In our model
the intersite Coulomb repulsion and exchange coupling can work as the effective
interaction for the spin-triplet paring. This effective interaction is enhanced
by the band hybridization, which is mediated by the interlayer transfers. We
investigate the possibility of this mechanism in the ground state and find that
the orbital dependent spin-triplet superconductivity is more stable than the
spin-singlet one for realistic parameters. This spin-triplet superconducting
state has horizontal line nodes on the Fermi surface.
