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The recently discovered high-T$_C$ superconductor La$_3$Ni$_2$O$_7$ hassparked renewed interest in the unconventional superconductivity. Here we studysuperconductivity in pressurized La$_3$Ni$_2$O$_7$ based on a bilayertwo-orbital $t-J$ model, using the renormalized mean-field theory. Our resultsreveal a robust $s^\pm-$wave pairing driven by the inter-layer $d_{z^2}$magnetic coupling, which exhibits a transition temperature within the sameorder of magnitude as the experimentally observed $T_c \sim 80$ K. We establisha comprehensive superconducting phase diagram in the doping plane. Notably, theLa$_3$Ni$_2$O$_7$ under pressure is found situated roughly in the optimaldoping regime of the phase diagram. When the $d_{x^2-y^2}$ orbital becomesclose to half-filling, $d-$wave and $d+is$ pairing can emerge from the system.We discuss the interplay between Fermi surface topology and different pairingsymmetries. The stability of the $s^\pm-$wave pairing against Hund's couplingand other magnetic exchange couplings is discussed.

High-T$_C$ superconductivity in $\mathrm{La_3Ni_2O_7}$ based on the bilayer two-orbital t-J model