The Casimir interaction of a sandwich structure was investigated, where the structure was formed by means of inserting a dispersive metamaterial slab between the metal slab and the dielectric substrate. Based on Casimir-Liftshitz theory, the radiation pressure of the vacuum fluctuation was calculated by the Maxwell tensor method, and the situation for the sandwich structure was numerically calculated and analyzed by the method of transfer matrix of the electromagnetic mode. The calculation results show that the Casimir force for two-slab structure may turn into repulsion for the sandwich structure by means of inserting a metamaterial slab to the previous bi-layer structure, therefore the thin metal slab can be levitated by the repulsive Casimir force. The influences of the metamaterial dispersive electromagnetic response properties and the dielectric substrate were discussed. It is seen that when the larger magnetic plasma frequency of the metamaterial, the smaller magnetic resonance frequency and the smaller dielectric constant of the dielectric substrate are taken, the greater repulsion force can be obtained in the sandwich structure. In addition, it is found that when the slab distance is increased to a certain extent, the restoring Casimir force can be obtained in the sandwich structure. For the formation of restoring force, it shows that when the smaller filling factor of the metamaterial, the larger layer separation and larger layer thickness are adopted, the restoring force in the sandwich structure will appear at farther slab separation position. The quantum levitation and the restoring force may guarantee the stability of the micro- and nano-electromechanical system devices, and show the new application prospect based on the radiation pressure of vacuum fluctuation.