  Within the framework of QED we investigate the inclusive J/\psi production at
$e^+e^-$ colliders. It is expected to be as a further test to the charmonium
production mechanisms and QED. We find that at the energies of CESR, BEPC, and
TRISTAN (e.g. 4.0 GeV \leq \sqrt s \leq 60 GeV), the contributions of the
concerned electromagnetic processes to the $J/\psi$ inclusive production are
great, even dominant, thus they greatly affect the observation of the
color-octet $J/\psi$ production signature at $e^+e^-$ colliders. The production
of \psi', being similar to that of J/\psi's, is roughly estimated, and its
influence on the observation of the color-octet J/\psi production signature in
e^+e^- collision is also discussed.
