  Double $J/\psi$ production in $e^+e^-$ collisions involving colour-octet
channels are evaluated up to order $\alpha^2\alpha_s^3$. Having implemented the
variation of the parameters ($m_c$, $\mu_r$ and long-distance matrix elements),
we found that the cross sections for producing double $J/\psi$ at B-factories
range from $-0.016$fb to $0.245$fb, which are even much smaller than that via
the colour-siglet mechanism. Accordingly, this result is consistent with the
measurement by the Belle and BABAR Collaborations.
