  We derive the fragmentation function (FF), which describes the probability
for a charm quark to emit a $D$ meson with a certain momentum fraction, in the
Nambu-Jona-Lasinio (NJL) model. The corresponding elementary FF is calculated
with the quark-meson coupling determined in the NJL model involving charm
quarks. The FF in the infinite momentum frame is constructed through the jet
process governed by the elementary FF, and then evolved to the charm scale, at
which it is defined. To prepare the FF suitable for an analysis of $D$ meson
production at CLEO, we further match the above FF to that in the finite
momentum frame at one loop in QCD. It is shown that the charm quark FF
including the finite momentum effects leads to theoretical results in agreement
with the CLEO data.
