  Within the Standard Model, we investigate the semi-leptonic weak decays of
$J/\psi$. The various form factors of $J/\psi$ transiting to a single charmed
meson ($D^{(*)}_{(d,s)}$) are studied in the framework of the QCD sum rules.
These form factors fully determine the rates of the weak semi-leptonic decays
of $J/\psi$ and provide valuable information about the non-perturbative QCD
effects. Our results indicate that the decay rate of the semi-leptonic weak
decay mode $J/\psi \to D^{(*)-}_{s}+e^{+}+\nu_{e}$ is at order of $10^{-10}$.
