  The $\gamma+\gamma\rightarrow J/\psi+c+\bar{c}$ inclusive process is an
extremely important subprocess in $J/\psi$ production via photon-photon
scattering, like at LEP\uppercase\expandafter{\romannumeral2} or various types
future electron-positron colliders. In this work we perform the
next-to-leading(NLO) QCD corrections to this process in the framework of
non-relativistic QCD(NRQCD) factorization formalism, the first NLO calculation
for two projectiles to 3-body quarkonium inclusive production process. By
setting the center-of-mass energy at LEP\uppercase\expandafter{\romannumeral2},
the $\sqrt{s}=197$ GeV, we conduct analyses of the $p_t^2$ distribution and
total cross section of this process at the NLO accuracy. It turns out that the
total cross section is moderately enhanced by the NLO correction with a $K$
factor of about 1.46, and hence the discrepancy between DELPHI data and
color-singlet(CS) calculation is reduced while the color-octet(CO)
contributions are still inevitable at this order. At the future Circular
Electron-Positron Collider(CEPC), the NLO corrections are found to be more
significant, with a $K$ factor of about 1.76.
