  Motivated by the recent discovery of high-temperature superconductivity in
bilayer La$_3$Ni$_2$O$_7$ under pressure, we study its electronic properties
and superconductivity due to strong electron correlation. Using the inversion
symmetry, we decouple the low-energy electronic structure into block-diagonal
symmetric and antisymmetric sectors. We find that the antisymmetric sector can
be reduced to a one-band system near half filling, while the symmetric bands
occupied by about two electrons are heavily overdoped individually. Using the
strong coupling mean field theory, we obtain strong superconducting pairing
with $B_{1g}$ symmetry in the antisymmetric sector. We propose that due to the
spin-orbital exchange coupling between the two sectors, $B_{1g}$ pairing is
induced in the symmetric bands, which in-turn boosts the pairing gap in the
antisymmetric band and enhances the high-temperature superconductivity with a
congruent $d$-wave symmetry in pressurized La$_3$Ni$_2$O$_7$.
