A Mach-Zehnder interferometer based on fiber core mismatch and core-offset splicing is proposed and experimentally tested for the simultaneous measurement of refractive index and temperature. The sensor structure consists of a multi-mode fiber segment with an up-taper structure and a core-offset joint as two coupled units. The up-taper increases the light energy propagating in the fiber cladding, which improves the fringe visibility. Wavelength shifts were recorded for two transmission dips, associated with variations in the temperature and refractive index, respectively, to build up a sensing matrix for the device. The experimental results show that the sensitivities to changes in the refractive index and temperature are -25.682 nm/RIU and 0.073 nm/℃ within the refractive-index range 1.3449-1.3797 and temperature range 25-65 ℃. The proposed sensor is easy to fabricate and has low cost, so we believe that it has application prospects for various types of multi-parameter detection, including temperature, refractive index, etc.