A highly sensitive Mach-Zehnder interferometer based on a twisted structure in seven-core fiber (SCF) for curvature measurement is investigated both theoretically and experimentally. The device is fabricated by splicing a segment of a twisted SCF with single-mode fibers by the over fusion method. An interference pattern of the straight sensor appears in the transmission spectra. When the sensor is bent, the wavelength shift of the interference pattern is induced, which may be used for curvature measurement through wavelength shift. In the experiment, SCFs with and without the twisted structure are tested, and the results are compared with wavelength-based sensitivities. The proposed twisted-SCF sensor offers a maximum curvature sensitivity of $ - {25.16}\,\,{{\rm nm/m}^{ - 1}}$-25.16nm/m-1 within the measurement range of ${0.5201 - 1.0071}\,\,{{\rm m}^{ - 1}}$0.5201-1.0071m-1, which is a 37-fold improvement compared with the previous works. The results also indicate that this highly sensitive all-fiber sensor offers great potential for realization of curvature measurement in the field of structural health monitoring.