This study presents a grating interferometric acoustic sensor based on a flexible polymer diaphragm. A flexible-diaphragm acoustic sensor based on grating interferometry (GI) is proposed through design, fabrication and experimental demonstration. A gold-coated polyethylene terephthalate diaphragm was used for the sensor prototype. The vibration of the diaphragm induces a change in GI cavity length, which is converted into an electrical signal by the photodetector. The experimental results show that the sensor prototype has a flat frequency response in the voice frequency band and the minimum detectable sound pressure can reach 164.8 µPa/√Hz. The sensor prototype has potential applications in speech acquisition and the measurement of water content in oil. This study provides a reference for the design of optical interferometric acoustic sensor with high performance.