A novel fiber interferometer sensor based on core-offset for simultaneously measuring refractive index and temperature is proposed. It makes a multimode fiber MMF2 left weld with a multimode fiber MMF1 which has a same core diameter and length in core-offset way, and right weld with a multimode fiber MMF3 which has a larger core diameter to be the sensor head. By observating the wavelength shifts of the interference dips, temperature and refraction index (RI) can be measured simultaneously since the core modes and the cladding modes have different sensitivities to the two parameters. The dips at 1536.98 nm and at 1545.24 nm are chosen to measure the temperature and the RI. Experiments indicate that the temperature sensitivities of the dips at 1536.98 nm and at 1545.24 nm are 0.105 nm/℃ and 0.052 nm/℃. The RI sensitivity coefficient of the dip at 1545.24 nm is 32.2 nm/RIU, whereas the dip at 1536.98 nm is insensitive. This fiber interferometer sensor can also be applied in other sensing fields and has good prospects.