All-fiber acousto-optic tunable filters (AOTFs) have advantages of wide wavelength tuning range, fast tuning speed and low insertion loss. The resonance wavelength of the all-fiber AOTF can be tuned by adjusting the driving frequency of the piezoelectric transducer (PZT). In general, the driving voltage needs to be tuned in wide range in the wavelength tuning process, due to the existence of resonance frequency of the PZT. In this work, we propose and demonstrate a stability-enhanced all-fiber AOTF based on multi-PZT, which can reduce the dependence on the resonant frequency of a single PZT. In the experiment, the acousto-optic coupling efficiency can maintain larger than 80%, when the resonance wavelength of the AOTF is tuned from 1400 nm to 1600 nm, under the condition of a fixed driving voltage. The high tuning stability of the proposed multi-piezoelectric driving configuration can facilitate the practical applications of the all-fiber AOTF, such as the laser wavelength tuning, wavelength-division-multiplexing optical communication, fast optical spectroscopy, and so on.