Based on the three-dimensional micromagnetic simulations, we present a method to tailor the microwave permeabilities of magnonic metamaterials cells by a designed nanoring structure. The results show that the permeabilities and resonant frequency are depended on the wall s thickness of nanorings. The underlying mechanism is ascribed to the presence of strong demagnetization fields, which are associated to the ring s wall. In addition, the products of magnetic susceptibility and resonant frequency are larger than that predicted from Snoek s law in polycrystalline particles. These results are direct manifestations of the bi-anisotropy model.