A scheme to construct analogical atoms using graphene nanostructures via quantum nonlinearity is proposed. Due to the strong field localization capability of graphene plasmons and the significant intrinsic nonlinearity of graphene, a strong nonlinear optical response can be realized even with single-photon excitation. In this process, the quantum vacuum localized plasmonic mode plays a crucial role in achieving the third-order multi-photon nonlinear effect. The eigenfrequency of the nanostructure can shift by an amount tens of times larger than the decay rate, causing the nanostructure cavity to exhibit atomic-like behaviors. Furthermore, multilevel atoms can be constructed through the interaction of composite graphene nanostructures. The parameters of these atoms can be manipulated by adjusting the nanostructure size, Fermi energy, and other parameters. This research holds significant potential for applications in highly integrated, controllable nanophotonics.