The linear ac transport of square-shaped graphene nanoconstriction devices are investigated, employing Buttiker’s ac transport theory. Based on Green’s function, the dynamic conductances taking account of both dc and ac contributions are presented. The square-shaped graphene nanoconstriction device displays semiconducting and resonance features in the transporting channels. The device responds capacitively or inductively to the external ac perturbations depending on the dynamic processes of the internal charges at the central nanoconstriction region. We show that as a result of the coupling and the band-mixing between the leads and the central constriction, the ac transport properties are sensitive to the geometry of the graphene systems.