  In nonrelativistic Quantum Chromodynamics (NRQCD), we study the
next-to-leading order (NLO) QCD radiative correction to the color-octet
$J/\psi$ inclusive production at B Factories. Compared with the leading-order
(LO) result, the NLO QCD corrections are found to enhance the short-distance
coefficients in the color-octet $J/\psi$ production $ e^+ e^-\to c \bar c
(^3P_0^{(8)} {\rm or} ^3P_0^{(8)})g$ by a factor of about 1.9. Moreover, the
peak at the endpoint in the $J/\psi$ energy distribution predicted at LO can be
smeared by the NLO corrections, but the major color-octet contribution still
comes from the large energy region of $J/\psi$. By fitting the latest data of
$\sigma(e^{+}e^{-}\to J/\psi+X_{\mathrm{non-c\bar{c}}})$ observed by Belle, we
find that the values of color-octet matrix elements are much smaller than
expected earlier by using the naive velocity scaling rules or extracted from
fitting experimental data with LO calculations. As the most stringent
constraint by setting the color-singlet contribution to be zero in
$e^{+}e^{-}\to J/\psi+X_{\mathrm{non-c\bar{c}}}$, we get an upper limit of the
color-octet matrix element, $<0| {\cal O}^{J/\psi}[{}^1S_0^{(8)}]|0> + 4.0 <0|
{\cal O}^{J/\psi} [{}^3P_0^{(8)}]|0>/m_c^2 <(2.0 \pm 0.6)\times 10^{-2} {\rm
GeV}^3$ at NLO in $\alpha_s$.
