A refractive index sensor based on a multi-core micro/nano fiber is proposed for low refractive index solutions. At first, the mode field distribution of the tapered multi-core fiber is analyzed with the finite element model (FEM). After that, the relationship between the refractive index sensitivity and the diameter of the multi-core micro/nano fiber is calculated. At last, four sensors with different sizes are explored, and when the taper length is 16.20 mm, the refractive index sensitivity of the sensor can reach 5815.50 nm/RIU, which agrees with the theoretical analysis. The refractive index measurement error is less than 0.5 ‰, which has a high practical application value. The longer the taper length is, the smaller the fiber diameter is. According to the theoretical analysis, when the fiber diameter is less than 4.864 μm, the structure sensor’s refractive index sensitivity is higher than 10000 nm/RIU. At the same time, when the sensor’s taper length is 15.99 mm, its temperature sensitivity is -0.1084 nm/℃. Compared with single-mode fiber, the sensor proposed here has the advantages of stability, compact structure, and high sensitivity, which has a potential in the field of seawater salinity measurement.