A fiber fabry-perot sensor for partial discharges measurement was studied on getting stable working points. The parameters of the sensor were optimized to achieve higher sensitivities. The working points could be stabilized illuminated by a tunable laser. For a senor, the cavity length of the sensor was determined by the tuning range of the tunable laser. Then, the reflectivity of the silica film was set to 1. Finally, the reflectivity of the fiber end was optimized by numerical simulations according to Gaussian beams and multi-beam interference theory. In experiments, a sensor was made with 28nm-FSR, 43μm-cavity length, the reflectivity of the silica film is above 0.97, and the reflectivity of the fiber end is 0.52. The losses of the cavity are 10 percent of the total energy. The fringe contrasts of the sensors arrive to 1. The sensor operates steadily illuminated by a tunable laser with 1530nm to 1565nm tuning range. The minimum detectable acoustic-pressure is about 1Pa. The performances of the sensor meet the demand of practical applications.