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In this letter, the periodic focusing effect of graded-index multimode fibers is used to improve the performance of fiberoptic Fabry-Perot (FFP) sensors. The maximum fringe contrast of the reflective spectrum of the FFP sensor in air is >32 dB. By detecting the fringe contrast variation and wavelength shift of the reflective spectrum, such an FFP sensor is used to measure the refractive index and temperature with sensitivities of ~45.05 dB/RIU and 11.5 pm/°C , respectively. It is also verified by the experiment that the simultaneous measurement of refractive index and temperature can be realized.