A novel fiber sensor for measuring strain and refractive index based on fiber Mach-Zehnder interference (MZI) principle and core-offset splicing technology was designed. The sensor was composed of a single mode fiber at both ends with core-offset fibers. Measurement of external refractive index and strain was realized based on sensitive characteristic of optical fiber cladding mode and core mode to strain and refractive index. The tested results indicate that wavelength of near infrared transmission spectrum shifts to shorter wavelength with a sensitivity about -7.00 pm/με at the dips 1585 nm under an axial strain 0-500 με; the wavelength shifts to shorter wavelength side with a sensitivity about -55.223 nm/RIU at the dips 1570 nm under 1.331-1.398 RIU refractive index, where RIU is refractive index unit. The fitting has a good linearity. This fiber sensor can also be applied to other sensing fields and have good prospects.