A superchirped moiré grating has multiple superimposed chirped Bragg gratings. We show that a superchirped moiré grating can be formed in an acousto-optic superlattice with a chirped fiber Bragg grating. There are multiple transmission peaks related to Fabry-Perot resonance in the transmission spectrum. The peak spacing is varied by the acoustic frequency. The proposed devices can be used as tunable multiple-passband transmission filters and switches.