Based on micro-Raman spectroscopy (μRS) and X-ray photoelectron spectroscopy (XPS), we study the structural damage incurred in monolayer (1L) and few-layer (FL) graphene subjected to atomic-layer deposition of HfO2 and Al2O3 upon different oxygen plasma power levels. We evaluate the damage level and the influence of the HfO2 thickness on graphene. The results indicate that in the case of Al2O3/graphene, whether 1L or FL graphene is strongly damaged under our process conditions. For the case of HfO2/graphene, μRS analysis clearly shows that FL graphene is less disordered than 1L graphene. In addition, the damage levels in FL graphene decrease with the number of layers. Moreover, the FL graphene damage is inversely proportional to the thickness of HfO2 film. Particularly, the bottom layer of twisted bilayer (t-2L) has the salient features of 1L graphene. Therefore, FL graphene allows for controlling/limiting the degree of defect during the PE-ALD HfO2 of dielectrics and could be a good starting material for building field effect transistors, sensors, touch screens and solar cells. Besides, the formation of Hf-C bonds may favor growing high-quality and uniform-coverage dielectric. HfO2 could be a suitable high-K gate dielectric with a scaling capability down to sub-5-nm for graphene-based transistors.