In this paper, a membrane stress continuously adjustable fiber optic acoustic sensor technology is proposed, in which the stress exerted on membrane can be flexibly adjusted by employing inverse piezoelectric effect of Lead zirconate titanate (PZT) tubular pedestal. Firstly, the response mechanism of stress on membrane is investigated theoretically. On this basis, the effect of adjustable stress on the flat response region and sensitivity of single mode-multimode-single mode (SMS) fiber optic acoustic sensor are studied experimentally. The experimental result reveals that the flat response region of sensor extends from 250 Hz to 450 Hz following with the continuous increase of membrane stress by changing the positive Direct Current (DC) voltage applied on PZT from 0 V to 100 V, meanwhile the sensitivity decreases gradually from 336.5 mV/Pa to 162.7 mV/Pa. The result also verifies that the average minimum detectable pressure (MDP) of sensor maintains at 0.54 mPa/Hz1/2 with a fluctuation of 0.08 mPa/Hz1/2 during the tuning process of membrane stress, which provides a flexible method for performance and applicability improvement of membrane-based fiber optic acoustic sensors.