  In this paper, we compute the total and differential cross sections for
$e^+e^- \to J/\psi+c+\bar{c}$ at the $B$ factories up to next-to-leading order
(NLO) corrections within the framework of nonrelativistic QCD factorization
theory. We then obtain an improved pQCD prediction for this process by using
the Principle of Maximum Conformality (PMC). We show the first time that the
PMC can be applied for any pQCD calculable observable at the total or
differential levels via a self-consistent way in perturbation theory. By the
recursive use of renormalization group equation, the resultant PMC series
satisfies all the requirements of renormalization group, which is free of
conventional renormalization scheme-and-scale ambiguities at any fixed-order
level. We thus obtain a more precise prompt total cross section at the NLO
level, e.g. $\sigma|_{\rm prompt}^{\rm PMC}=
0.565^{+0.144}_{-0.125}~\text{pb}$. Here the uncertainty is the squared average
of those from the $\alpha_s$ fixed-point uncertainty $\Delta\alpha_s(M_Z)$, the
uncertainty of charm quark mass $\Delta m_c$, and an estimated contribution of
the uncalculated NNLO-terms as predicted by the Pad\'{e} approximation
approach. The differential cross sections $d\sigma/dP_{J/\psi}$,
$d\sigma/d|\cos \theta|$, and $d\sigma/dz$ for $e^+e^- \to J/\psi+c+\bar{c}$
are further examined. Those results show that by further considering the
feed-down contributions, the PMC predictions show better agreement with the
Belle measurements.
