A Mach-Zehnder interferometer based on multi-core fiber, which composes of a single-mode, multi-core, multi-mode, and single-mode fiber, is proposed in this study. In the proposed interferometer, the multi-mode fiber functions as a coupler, whereas the single-mode fiber and the multi-core fiber form an asymmetric structure by offset splicing. Further, the bending and axial strain characteristics of the interferometer are studied experimentally. The experimental results show that the wavelength of the transmission spectrum of the interferometer is linearly shifted when the interferometer bends. The wavelength change can be used to modulate the curvature, and the maximum sensitivity of bending curvature is -16.88 nm/m^-1. When the interferometer bends to the directions of 0° and 180°, the wave-valley wavelengths shift in the opposite direction, allowing for a preliminary determination of the bending direction. In addition, the interferometer is also sensitive to axial strain. By using the measured bending curvature and axial strain sensitivity to construct the measurement matrix, the simultaneous measurement of bending curvature and axial strain can be realized, and the cross sensitivity can be eliminated.