  We investigate the leading twist generalized transverse momentum dependent
parton distributions (GTMDs) of the unpolarized and longitudinally polarized
gluons in the nucleon. We adopt a light-front gluon-triquark model for the
nucleon motivated by soft-wall AdS/QCD. The gluon GTMDs are defined through the
off-forward gluon-gluon generalized correlator and are expressed as the overlap
of light-cone wave functions. The GTMDs can be employed to provide the
generalized parton distributions (GPDs) by integrating out the transverse
momentum. The Fourier transform of the GPDs encodes the parton distributions in
the transverse position space, namely, the impact parameter dependent parton
distributions (IPDs). We also calculate the three gluon IPDs corresponding to
the GPDs $H^g$, $E^g$ and $\widetilde{H}^g$, and present their dependence on
$x$ and $b_\perp$, respectively.
