In this paper, an all fiber acousto-optic tunable filter based on superimposed fiber Bragg gratings (SFBG-AOTF) is demonstrated and studied. Compared to the normal fiber Bragg gratings based all fiber acousto-optic tunable filter, SFBG-AOTF can modulate the two optical resonant wavelengths of the gratings synchronously. The spectrum of SFBG-AOTF at various acoustic frequencies and under acoustically induced strains, has been analyzed theoretically. Based on simulation results, one can find that each order of the secondary reflection peak is symmetrical with respect to the two primary reflection peaks with SFBG as the center, and the resonant wavelength spacing between the primary reflection peak and the secondary reflection peak which is modulated by the former, is proportional to the acoustic frequency. But the resonant wavelength between the same order secondary reflection peaks which are modulated by two different primary reflection peaks, is independent of the acoustic frequency. The acoustically induced strains mainly affect the variation of the reflectivities of the primary and secondary reflection peaks. In the experiment, the spectra of SFBG-AOTF with acoustic frequencies of 390 and 710 kHz, are measured. The variation trend of the experimental results accords well with the simulated one.