  Next-to-Leading-Order(NLO) QCD corrections to double J/psi production in
e^+e^- annihilation at sqrt{s}=10.6 GeV are calculated. We find that they
greatly decrease the cross section, with a K factor (NLO/LO) ranging from -0.31
to 0.25 depending on the renormalization scale. Although the renormalization
scale dependence indicates a large uncertainty, when combined with the NLO QCD
corrections to J/psi + eta_c production, it can explain why the double J/psi$
production could not be found at B factories while the J/psi + eta_c production
could, despite the fact that cross section of the former is larger than that of
the latter at LO by a factor of 1.8.
