The invention discloses a film bulk acoustic wave resonator and a film bulk acoustic wave filter. The thin film bulk acoustic wave resonator comprises a silicon substrate, a support layer and a firstbottom electrode layer, a temperature drift layer and a sandwich piezoelectric stack structure, the supporting layer is combined on the surface, provided with the groove, of the substrate in a laminated manner; a closed cavity is defined by the supporting layer and the groove; wherein the first bottom electrode layer is laminated and combined on the surface, deviating from the substrate, of the supporting layer, the temperature drift layer is laminated and combined on the surface, deviating from the supporting layer, of the first bottom electrode, and the sandwich piezoelectric stack structureis laminated on the surface, deviating from the first bottom electrode layer, of the temperature drift layer. The film bulk acoustic wave filter comprises the film bulk acoustic wave resonator. The film bulk acoustic wave filter and the resonator are low in consumption, small in temperature coefficient, low in temperature drift, high in power bearing capacity, high in working frequency, high in electromechanical coupling coefficient, good in compatibility and good in Q value.