Based on the band gap theory of periodic structure, this article proposes a new variable cross-section periodic structure support made of acrylonitrile-butadiene-styrene. The band gap characteristics of the periodic structure support were studied experimentally. According to the basic theory of band gap calculation, two kinds of supports with the same installation size were designed, and they were manufactured by 3D printer. Then, the displacement–load curve and the vibration characteristic curves of the periodic structure support were obtained through simulation analysis. The band gap range of the two supports was measured by hammer excitation, and the accuracy of the finite element model was verified by comparison with the experiment results. Finally, the response curve of the periodic structure support with variable cross-section every 100 Hz was obtained by excitation of the shaker, which verified the vibration isolation effect of the measured band gap. The results show a band gap in the support of the variable cross-section periodic structure, compared with the support of the non-periodic structure. If the vibration frequency is within the band gap frequency, the vibration will be significantly attenuated.