  We propose the color-octet mechanism combined with the two gluon exchange
model for the diffractive $J/\psi$ production in hadron collisions. In the
leading logarithmic approximation (LLA) in QCD, we find that the diffractive
$J/\psi$ production rate is related to the off-diagonal gluon density in the
proton and to the nonperturbative color-octet matrix element of $J/\psi$. The
rate is found to be very sensitive to the gluon density at very small values of
$x$ (down to $x=O(10^{-6})$). As a result, this process may provide a wide
window for testing the two-gluon exchange model, and may be particularly useful
in studying the small $x$ physics. And it may also be a golden place to test
the color-octet mechanism proposed by solving the $\psi'(J/\psi)$ surplus
problem at the Tevatron.
