In this paper, an all-fiber Mach-Zehnder interferometer (MZI) based on a non-zero dispersion-shifted fiber (NZ-DSF) is presented. The MZI was implemented by core-offset fusion splicing one section of a NZ-DSF fiber between two pieces of single mode fibers (SMFs). Here, the NZ-DSF core and cladding were used as the arms of the MZI, while the core-offset sections acted as optical fiber couplers. Thus, a MZI interference spectrum with a fringe contrast (FC) of about 20 dB was observed. Moreover, its response spectrum was experimentally characterized to the torsion parameter and a sensitivity of 0.070 nm/° was achieved. Finally, these MZIs can be implemented in a compact size and low cost.