  Based on the nonrelativistic QCD factorization approach, ${\mathcal
O}(\alpha_s v^2)$ corrections to $\jpsi$ plus $\eta_c$ production in $e^+e^-$
annihilation at $\sqrt{s}=10.6 \gev$ is calculated in this work. The numerical
results show that the correction at $\alpha_s v^2$ order is only about a few
percent for the total theoretical result. It indicates that the perturbative
expansions for the theoretical prediction become convergence and higher order
correction will be smaller. The uncertainties from the long-distance matrix
elements, renormalization scale and the measurement in experiment are also
discussed. Our result is in agreement with previous result in ref [1].
