To achieve high accuracy and high sensitivity measurement of refractive index, an asymmetric micro-nano fiber Fabry-Perot resonator is fabricated using micron size hydrofluoric(HF)-acid droplet chemical etching method. The fabricated structure is featured with small size, low loss, large birefringence and high Q value. The guided modes along the orthogonal polarizations present different refractive index (RI) responses. The measured RI sensitivities are 133.8 nm/RIU and 117.1 nm/RIU for the modes along the fast and slow axis, respectively. The temperature sensitivity is 0.012 nm/°C for the two polarization modes. The temperature independent refractive index measurement can be realized by monitoring the wavelength difference of two polarized light with spectrometer. Experiment investigation is carried out with optical fiber sensors with different FP cavity parameters. Results show that the smaller the cavity diameter of fiber FP sensor is, the higher the corrosion rate is, and the higher the refractive index sensitivity is.