Due to its excellent mechanical, electrical and optical sensing properties, graphene is expected to become a functional sensitive material for the next generation of wearable electronic devices. Although graphene-based optical fiber Fabry-Perot (F-P) acoustic sensor has the advantages of high sensitivity, miniaturization and anti-electromagnetic interference, it will be affected by temperature drift. The influence of temperature on the sensor mainly changes the F-P cavity length, thereby causing the working point drift and then the change in the optical sensitivity of the sensor. Also, the prestress of graphene film is adjusted. In this paper, an optical fiber F-P acoustic sensor using graphene diaphragm was fabricated and then acoustic test demonstrated the change of mechanical properties of suspended graphene diaphragm, thus achieving the increase of the mechanical sensitivity from 1.80 nm/Pa to 2.44 nm/Pa at 1 kHz.