The $gamma+gammarightarrow J/psi+c+bar{c}$ inclusive process is an extremely important subprocess in $J/psi$ production via photon-photon scattering, like at LEPuppercaseexpandafter{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 LEPuppercaseexpandafter{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.
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