A narrowband fast tunable acousto-optic filter is proposed and demonstrated based on the acoustically-induced birefringence of dispersion compensating fiber. The band-pass and band-stop filtering characteristics of the filter are realized through the mode coupling caused by the acoustic vibration generated by the device. At the same time, the single wavelength filtering effect with the bandwidth of about 7nm is realized by optimizing the operating distance of Acousto-Optic Interaction (AOI) length. The constructed filter obtains the advantages of narrow band, fast tuning speed, single wavelength, compact size, simple fabrication and zero frequency shift. It has potential applications in the fields of tunable lasers, wavelength division multiplexing optical communication and optical signal processing.