  Based on the non-relativistic quantum chromodynamics factorization framework,
we study the inclusive $J/\psi$ photoproduction at the future high energy
$e^+e^-$ collider, International Linear Collider(ILC), where the initial
photons come from the back-scattering of laser and electron (positron). The
intermediate states,
$c\bar{c}$$({}^3\!S_1^{[\textbf{1}]}$,${}^1\!S_0^{[\textbf{8}]}$,${}^3\!S_1^{[\textbf{8}]}$,${}^3\!P_{0,1,2}^{[\textbf{8}]})$,
and resolved photoproduction processes are considered. Numerical results show
that the cross section of $J/\psi$ photoproduction at the ILC could be very
large, and the single resolved process via $c\bar{c}({}^1\!S_0^{[\textbf{8}]})$
intermediate state dominates primarily the production. We also present various
kinematic distributions for $J/\psi$ photoproduction. Combining the high
luminosity of the collision, $J/\psi$ photoproduction at the ILC shall provide
a good platform to test the NRQCD factorization.
