  The gravitationally enhanced friction can reduce the speed of the inflaton to
realize an ultra-slow-roll inflation, which will amplify the curvature
perturbations. The amplified perturbations can generate a sizable amount of
primordial black holes (PBHs) and induce simultaneously a significant
background gravitational waves (SIGWs). In this paper, we investigate the
primordial non-Gaussianity of the curvature perturbations in the inflation with
gravitationally enhanced friction. We find that when the gravitationally
enhanced friction plays a role in the inflationary dynamics, the
non-Gaussianity is noticeably larger than that from the standard slow-roll
inflation. During the regime in which the power spectrum of the curvature
perturbations is around its peak, the non-Gaussianity parameter changes from
negative to positive. When the power spectrum is at its maximum, the
non-Gaussianity parameter is near zero ($\sim \mathcal{O}(0.01)$). Furthermore,
the primordial non-Gaussianity promotes the formation of PBHs, while its effect
on SIGWs is negligible.
