  Next-to-Leading-Order(NLO) QCD corrections to J/jpsi plus eta_c production in
e+e- annihilation at sqrt{s}=10.6 GeV is calculated in this paper, and an
analytic result is obtained. By choosing proper physical parameters, a K factor
(ratio of NLO to LO) of about 2, which is in agreement with the result in
Ref.\cite{Zhang:2005ch}, is obtained. Our results show that the
Next-Next-to-Leading-Order(NNLO) corrections might be quite large. The plot of
the K-factor vs the center-of-mass energy sqrt{s} shows that it is more
difficult to obtain a convergent result from the perturbative QCD without
resummation of ln(s/m_c) terms as the sqrt{s} becomes larger.
