  We calculate the next-to-leading-order (NLO) QCD corrections to $e^+e^-\to
J/\psi g g$ via color singlet $J/\psi(^3{-0.8mm}S_1)$ at the B factories. The
result shows that the cross section is enhanced to $0.373\pb$ by a K factor
(NLO/LO) of about 1.21. By considering its dependence on the charm quark mass
and renormalization scale, the NLO cross section can range from 0.294 to
$0.409\pb$. Further including the $\psi^\prime$ feed-down, $\sigma(e^+e^-\to
\jpsi X(\mathrm{non} c\bar{c}))$ is enhanced by another factor of about 1.29
and reaches $0.482\pb$. In addition, the momentum distributions of $J/\psi$
production and polarization are presented. Recent measurements from Belle agree
well with our prediction for the cross section and momentum distribution. It is
expected that this process can serve as a very good channel to clarify the
$J/\psi$ polarization puzzle by performing further experimental measurements.
