A periodic isolator possesses of high static stiffness and broad low frequency band gap has been designed by using the curved beam which has the characteristic of coupled radial-tangential stiffness and has the potential of conversion of waves. The multi-layer periodic isolator is composed of rigid plates and curved beams. For the structure supported in the single opposite edges, the expressions of the band gap structure of periodic structure which possesses interior coordinates and the solving process of forced response by substructure synthesis method are presented and validated. The proposed substructure synthesis method is helpful in modeling the periodic structures that have a large number of periodic unit cells. The relations between the initial frequency/the end frequency of the band gap and the natural frequencies, the mode shapes of the periodic structure are studied. And the influence of parameters of curved beam on the initial frequency/the end frequency of the band gap is studied in detail. The experiment to test driving-point and transfer mobilities of a periodic isolator is carried out. The results demonstrate that the periodic isolator composed of curved beams has wide band gap. The agreement between experiment results and theoretical prediction is acceptable.