This paper investigates the magnetism and superconductivity in the $t-J$ model of $La_3Ni_2O_7$ under multiband Gutzwiller approximation. The study focuses on a bilayer two-orbital model, where both $d_{z^2}$ and $d_{z^2-y^2}$ orbitals are active, as revealed by DFT calculations. The inter-orbital super-exchange process between these orbitals leads to ferromagnetic coupling within layers, competing with conventional antiferromagnetic coupling. As hole doping increases, the system transitions from a G-type antiferromagnetic (G-AFM) state to an A-type antiferromagnetic (A-AFM) state. The inter-layer superconducting pairing of $d_{z^2-y^2}$ orbitals dominates due to the large hopping parameter of $d_{z^2}$ along vertical inter-layer bonds and significant Hund's coupling. The G-AFM state and superconductivity can coexist in the low hole doping regime. The paper also analyzes the impact of inter-layer hopping amplitude on the system properties, showing that increasing this parameter enhances the optimal doping and magnitude of superconducting pairing order. The results provide insights into the complex physics of $La_3Ni_2O_7$, including the interplay between magnetism and superconductivity.This paper investigates the magnetism and superconductivity in the $t-J$ model of $La_3Ni_2O_7$ under multiband Gutzwiller approximation. The study focuses on a bilayer two-orbital model, where both $d_{z^2}$ and $d_{z^2-y^2}$ orbitals are active, as revealed by DFT calculations. The inter-orbital super-exchange process between these orbitals leads to ferromagnetic coupling within layers, competing with conventional antiferromagnetic coupling. As hole doping increases, the system transitions from a G-type antiferromagnetic (G-AFM) state to an A-type antiferromagnetic (A-AFM) state. The inter-layer superconducting pairing of $d_{z^2-y^2}$ orbitals dominates due to the large hopping parameter of $d_{z^2}$ along vertical inter-layer bonds and significant Hund's coupling. The G-AFM state and superconductivity can coexist in the low hole doping regime. The paper also analyzes the impact of inter-layer hopping amplitude on the system properties, showing that increasing this parameter enhances the optimal doping and magnitude of superconducting pairing order. The results provide insights into the complex physics of $La_3Ni_2O_7$, including the interplay between magnetism and superconductivity.