In order to improve the sensitivity of optical fiber partial discharge detection, a design scheme of optical fiber Fabry Perot(F-P) sensor with beam supported membrane structure for partial discharge detection is proposed. The response frequency, sensitivity, linear range and flatness of the sensor are simulated and analyzed under different geometric parameters. The simulation results show that, compared with the optical fiber F-P sensor with circular membrane structure, the optical fiber F-P sensor with beam supported membrane structure not only shows higher sensitivity(nearly three times higher sensitivity in some cases) and wider frequency working range, but also improves the linear range and flatness of the sensor.