A kind of hybrid fiber interferometer consisting of a fiber Sagnac interferometer (FSI), a closed-cavity Fabry-Perot interferometer (FPI), and an open-cavity FPI is proposed for generating combined-Vernier-effect. Through adjusting the polarization-maintaining fiber (PMF) length of the FSI, the free spectral range (FSR) is tailored to be similar to that of the parallel-connected reference FPI for producing the first Vernier effect, of which the spectrum is used to match the sensing FPI spectrum for obtaining the second Vernier effect. Noticeable lower and upper spectral envelopes are achieved in the first and second Vernier effects, respectively, so called the combined-Vernier spectrum. Accessibly, the upper envelope is only sensitive to the refractive index (RI) owing to the characteristics of the open-cavity FPI, while the lower one is immune to the RI and employed to detect the temperature by taking advantage of the FSI. Most importantly, the sensitivities of RI and temperature can be significantly improved simultaneously without crosstalk. The experimental results show that the RI sensitivity is -19844.67 nm/RIU and the temperature sensitivity is -46.14 nm/°C, which can be used for high-precision temperature and RI simultaneous measurement.