  In this paper, we study the next-to-next-to-leading-order (NNLO) QCD
corrections for the process $e^+e^- \to J/\psi+J/\psi$ at the $B$ factories. By
including the NNLO corrections, the cross section turns negative due to the
poor convergence of perturbative expansion. Consequently, to obtain a
reasonable estimation for the cross section, the square of the amplitude up to
NNLO is used. In addition, the contributions from the bottom quark and the
light-by-light part, which are usually neglected, are also included. The final
cross section is obtained as $1.76^{+2.42}_{-1.66} ~{\rm fb}$ at a
center-of-mass energy of $\sqrt{s}=10.58$ GeV. Our result for total cross
section and differential cross section could be compared with precise
experimental measurement in future at the $B$ factories.
