  The gluon fragmentation function of $g \to h_c$ at leading order of strong
coupling constant $\alpha_s$ and typical velocity $v$ is calculated in the
framework of NRQCD, of which the contributions from both color-singlet and
-octet processes are taken into account and hence the result is infrared safe.
It is found that the fragmentation probability of a high energy virtual gluon
to split into $h_c$ is about $7.1\times 10^{-7}$. The analytic fragmentation
function presented in this work can be employed to the study of $h_c$
production in large transverse momentum at hadron colliders, such as Large
Hadron Collider(LHC), and is also applicable for the study of $h_b$
hadronproduction.
