  We study the leading twist gluon generalized parton distributions (GPDs) and
the gluon angular momentum inside the proton within a light-cone spectator
model. Using the light-cone wave functions derived from the model, we provide
the expressions of these distributions at the particular kinematical point
$\xi=0$ in the overlap representation. The numerical results of the $H^g$,
$E^g$, $\tilde{H}^g$, $H_T^g$ and $E_T^g$ as functions of $x$ at different
$\Delta_T$ are presented. Particularly, $H^g$, $\tilde{H}^g$ at non-zero
$\Delta_T$ are different from their forward counterparts, the unpolarized
distribution $f_1^g$ and the helicity distribution $g_1^g$, respectively. We
also obtain the total angular momentum of the gluon contributed to the proton
spin $J^g=0.19$, which is consistent with the recent lattice calculation after
the uncertainties is considered. The kinetic orbital angular momentum is also
calculated and is negative in our model.
