In this paper, the Mach-Zehnder interferometer (MZI) based on ring-core fiber was proposed and manufactured. Benefiting from the identical diameters of ring-core fiber, no-core fiber, and single-mode fiber, the MZI fiber sensor can be prototyped by sandwiching the ring-core fiber between the no-core fiber and the single-mode fiber (SMF). With the proposed specific structure of the ring-core fiber, the simultaneous measurement of temperature and curvature was achieved with the MZI sensor by means of monitoring the wavelength shift of interference dips. Experimental results have shown that the sensitivity of curvature sensing could reach up to -3.68 nm/m-1 in the range from 1.3856 m-1 to 3.6661 m-1 with high linearity of 0.9959. Meanwhile, the maximum temperature sensitivity is measured to be 72 pm/°C with a fairly good linearity response of 0.9975. In addition, by utilizing the 2×2 matrix algorithm, the dual demodulation of temperature and curvature can be readily realized for the purpose of direct sensing. It is believed that the proposed special structure-based MZI sensor may show great potential applications in the field of fiber-optics sensing and structural health monitoring (SHM).