We propose a novel refractive index sensor based on Michelson interferometer by using double-core microfiber. Through the reflection of the end and taper of double-core fiber (DCF), the Michelson interference spectrum is formed. Owing to the structure characteristic of double-core microfiber, this interferometer can achieve the measurement of refractive index (RI) and temperature. The experimental results show that the refractive index sensitivity of the interferometer is 2 377.80 nm/RIU at the diameter of the taper waist of 8.76 μm. In the temperature ranges from 30 °C to 60 °C, the temperature sensitivity is 0.070 48 nm/°C. This sensor has the advantage of high refractive index sensitivity.