The paper presents the design and mathematical model of a ZnO-based MEMS acoustic sensor. The structure consists with a 3.0 μm thick piezoelectric ZnO layer sandwiched between a pair of aluminum electrodes on a 30 μm thick silicon diaphragm. The size of silicon diaphragm is 3.1 x 3.1 mm2. Resonance frequency of the structure is determined using harmonic analysis by ANSYS and found to be 41.8 KHz. Sensitivity of acoustic sensor with and without the effect of residual stress are obtained as 334.7μV/Pa and 221.6μV/Pa respectively. The proposed model of the acoustic sensor operated over a wide frequency range from 30 Hz to 8 kHz.