Theoretical expressions for analyzing the refractive-index sensitivity of the hybrid optical fiber Fabry-Pérot sensor is developed. Influence of the experimental parameters on the measurement sensitivity is discussed. Hybrid optical fiber Fabry-Pérot sensor is fabricated by chemically etching a graded-index multimode fiber (GI-MMF), fusion splicing it into a single mode fiber, and cleaving the GI-MMF. The fringe contrast exceeds 30 dB and the corresponding measurement sensitivity of refractive index is about 45 dB per refraction index unit. Experimental results are in good agreement with the theoretical ones. It is indicated by the numerical simulations that the performance of this kind of sensor can be further improved.