  To testify the validity of the perturbative QCD (pQCD) and investigate its
application range, one should look for a suitable process to do the job. $B\to
J/\psi D$ is a promising candidate. The linear momentum of the products is
relatively small, so that there may exist a region where exchanged gluons are
soft and the perturbative treatment may fail, so that the non-perturbative
effect would be significant. We attribute such non-perturbative QCD effects
into the long-distance final state interaction (FSI) which is estimated in this
work. We find that the contribution from the FSI to the branching ratio is
indeed sizable and may span a rather wide range of $10^{-6}\sim 10^{-5}$, and
cover a region where the pQCD prediction has the same order. A more accurate
measurement on its branching ratio may provide important information about the
application region of pQCD and help to clarify the picture of the inelastic
rescattering (i.e. FSI) which is generally believed to play an important role
in B decays.
