We fabricate a microelectromechanical systems (MEMS) microphone that incorporates a graphene-based membrane that vibrates in response to acoustic forcing. We employ a novel fabrication process, where a graphene/poly(methyl methacrylate) (PMMA) bilayer membrane is transferred over a cavity on a separate chip before being affixed to the surface of another chip containing an electrode, resulting in the fabrication of a moveable capacitor with a membrane-to-electrode gap of 8 $\mu \text{m}$ . The gap, which is less than half the size of other reported graphene membrane-based audio transducers, allows for the device to operate with the low-DC bias voltages of about 1 V and, when integrated with a custom-designed readout circuit, demonstrates a sensitivity to sound pressure between 0.1 and 10 mV/Pa across the range 100 Hz–20 kHz. As well as a sensitivity that is comparable with the previous work, the flat frequency response is stable when the sound pressure is varied between 70 and 80 dB SPL , with the sensitivity value not varying by more than 0.2 mV/Pa.