  We present a model calculation of the T-odd transverse momentum dependent
(TMD) gluon fragmentation functions for a spin-1/2 hadron. Our model is based
on the postulation that a time-like off-shell gluon can fragment into a hadron
and a single spectator particle, which is considered to be on-shell. We
consider the effect of the gluon exchange to calculate all necessary one-loop
diagrams for the gluon-gluon correlation functions. Two out of four one-loop
diagrams give sizeable contributions to the fragmentation functions. We obtain
analytical expressions for the four T-odd TMD fragmentation functions of the
gluon. We also provide numerical results on the z-dependence and
$k_T$-dependence of the fragmentation functions.
