The stereodynamics of the reaction Au+H$_2$ have been performed by using quasi-classical trajectory (QCT) method on a global potential energy surface created by Zanchet et al. at the collision energy of 1.8, 2.2, 3.0 eV. The calculation on $P(θ_r),$ $P(\phi_r),$ and $P(θ_r,\phi_r)$ and four polarization-dependent differential cross sections (PDDCSs) in the center-of-mass (CM) indicate the dependence of the product polarization on collision energies. The product rotational angular momentum vector $j'$ is symmetric and perpendicular to $k$ direction according to the $P(θ_r)$ distributions. The $P(\phi_r)$ distributions around $\phi_r=270^{\circ}$ indicate that the rotational angular momentum vectors not only aligned along the y-axis direction, but also oriented to the y-axis negative direction. For the lower collision energy of 1.8eV, the ${\rm PDDCS}_{00}$ is symmetric on the forward and backward scattering, probably due to the long lifetime complex created in the insertion reaction, while for the increasing collision energies, the prominent forward scattering is all on account of that the reaction is controlled by direct stripping.