We theoretically investigate the intensity-dependent optical nonlinearity in graphene-aided D-microfiber, by tuning the chemical potential of graphene and varying radial distance and radii of the D-microfiber. Utilizing an interplay between graphene and the enhanced evanescent field of a guided mode in the waveguide of interest, the net utility of nonlinear coefficient is harnessed up to a very high value of 106 W − 1 m − 1 . Importantly, which is ∼ two orders of magnitude larger than in PMMA–graphene–PMMA waveguide. The highly dispersive nature of the waveguide, D ∼ 103 ps/nm-km, and large nonlinear figure-of-merit, FOM NL ∼ 1.29, have raised the possibilities of utilizing slow light structures to operate devices at few watts power level with microscale length. These studies have opened one window towards the next-generation all fiber-optic graphene nonlinear optical devices.