A highly sensitive optical fiber Mach-Zehnder interference curvature sensor based on MMF-GIMMF-MMF, which was made by sandwiching the graded-index multimode fiber (GIMMF) between two pieces of very short stepped-index multimode fibers (SIMMFs) spliced with input-single-mode fiber (SMF) and output-SMF, respectively, was proposed. The core diameter of the SIMMFs and GIMMF was 105 µm and 50 µm, respectively, and cladding diameter of them were both 125 µm. The sensing principle of the MMF-GIMMF- MMF sensors and the influences of structure parameters on the interference spectrum characteristics were theoretically analyzed in detail. Experimental results showed that when the length of the GIMMF was short enough (usually ≤ 10 mm), interference spectrum was induced by the interaction between the core modes and the low-order cladding modes due to the special structure of the designed Mach-Zehnder interferometer. Intensity of the interference valleys was highly sensitive to the applied bending but nearly independent of the surrounding temperature, on the contrary, the dip wavelength showed negligible sensitivity to the applied bending but relatively high temperature sensitivity. Thus, a temperature- independent curvature sensor could be realized by tracing the intensity variation of interference valley. In addition, different interference valley exhibited different intensity-based curvature sensitivity, providing more options for curvature sensing applications. Especially, total length of the sensor could be as short as 3 mm with length of GIMMF and SIMMFs only 1mm, the maximum curvature sensitivity could reach up to -78.75 dB/m-1 in the small curvature range of 0-2.36 m-1. Owing to its compact size, easy fabrication, good reproducibility and low cost, the proposed sensor is promising for bending-related high-precision engineering applications.