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A refractive index (RI) sensor based on micro-nano fiber (MN-fiber) with chirped fiber Bragg grating (CFBG) Fabry--Perot cavity (FP-cavity) for a microfluidic chip has been proposed. A single -mode fiber is drawn by hydrogen flame heading come into MN-fiber. Two CFBGs are written into this MN-fiber by the ultraviolet (UV) laser mask exposure method. One is at the tapered region, another is at the micro-nano region. Then a micro-nano fiber with chirped fiber Bragg grating (MN-CFBGs) FP-cavity sensor is formed. The Bragg reflection wavelengths of two CFBGs are 1620 nm, 3-dB bandwidth are above 50 nm. The reflectance of two CFBGs are 70% and 99%, respectively. The effects of reflectivity and bandwidth of the CFBGs FP-cavity, diameter and length of MN-fiber with this sensor's optical properties are analysed is and discussed. This sensor is embedded in a microfluidic chip and the MN-fiber region is immersion microfluid in different channels. The experimental results show that refractive index sensitivity of the sensor is --986 nm/refractive index unit (RIU), and the signal of the sensor has little noise. The CFBG-FP sensor not only has high sensitivity and lager measurement range, but also high contrast resonance signal and stability. [ABSTRACT FROM AUTHOR]