  Possible high-$T_c$ superconductivity (SC) has been found experimentally in
the bilayer material La$_3$Ni$_2$O$_7$ under high pressure recently, in which
the Ni-$3d_{3z^2-r^2}$ and $3d_{x^2-y^2}$ orbitals are expected to play a key
role in the electronic structure and the SC. Here we study the two-orbital
electron correlations and the nature of the SC using the bilayer two-orbital
Hubbard model downfolded from the band structure of La3Ni2O7 in the framework
of the dynamical mean-field theory. We find that each of the two orbitals forms
$s_\pm$-wave SC pairing. Because of the nonlocal inter-orbital hoppings, the
two-orbital SCs are concomitant and they transition to Mott insulating states
simultaneously when tuning the system to half filling. The Hund's coupling
induced local inter-orbital spin coupling enhances the electron correlations
pronouncedly and is crucial to the SC.
