  We calculate the next-to-leading order (NLO) radiative correction to the
color-octet $h_c$ inclusive production in $e^+e^-$ annihilation at Super $B$
factory, within the nonrelativistic QCD factorization framework. The analytic
expression for the NLO short-distance coefficient (SDC) accompanying the
color-octet production operator $\mathcal{O}_8^{h_c}(^1S_0)$ is obtained after
summing both virtual and real corrections. The size of NLO correction for the
color-octet production channel is found to be positive and substantial. The NLO
prediction to the $h_c$ energy spectrum is plagued with unphysical endpoint
singularity. With the aid of the soft-collinear effective theory, those large
endpoint logarithms are resummed to the next-to-leading logarithmic (NLL)
accuracy. Consequently, further supplemented with the non-perturbative shape
function, we obtain the well-behaved predictions for the $h_c$ energy spectrum
in the entire kinematic range, which awaits the examination by the forthcoming
Belle II experiment.
