An acoustic sensor based on balloon-shaped microfiber Mach-Zehnder Interferometer (BSMZI) is proposed and demonstrated. The BSMZI is constructed by bending a tapered polarization-maintaining fiber (PMF), which has the interference phenomenon due to the phase difference between the fundamental mode and cladding modes of the balloon-shaped loop structure. When placing the sensor in front of a loudspeaker and using a fiber Bragg grating (FBG) as the signal reflector, the transmission spectra of the sensor can be changed with the acoustic signals correspondingly. Furthermore, by changing the bending radius of the BSMZI, the maximum sensitivity of the sensor is 115 mV/Pa, and the minimum detection pressure of the noise limit is 2.1 mPa/√Hz when the acoustic frequency range change from 100 Hz to 2000 Hz. The experimental results show that the sensor has a good ability in acoustic detection and has potential application in the fields of nuclear magnetic medical treatment and security interception.