A theoretical model based on the ray-transfer-matrix method is developed for explaining the principle of a graded-index multimode fiber (GI-MMF) based hybrid fiber Fabry-Perot (GI-FFP) sensor. It is verified by the numerical simulations and experimental results that the high fringe contrast of the reflective spectrum of the sensor is due to the periodic self-focusing effect of the GI-MMF. The influence of the GI-MMF length on the shape of reflective spectrum and corresponding maximum fringe contrast are investigated. Experimental results are in good agreement with the theory. A typical GI-FFP sensor is fabricated and its response to the external refractive index is measured with a maximum sensitivity of approximately 160 dB/RIU (Refractive Index Unit).