A bandwidth tunable Mach-Zehnder interferometer (MZI) based on tapered-drawing fiber Bragg grating is presented. The two sides of this microfiber-assisted MZI are the tapered micro chirped long period fiber gratings (CLPG) , which are symmetrical about the central waist. The period and refraction index of the grating after fused tapering are modelled and simulated. The refractive index test results show that the relationship between the refractive index of NaCl solution and the reciprocal of passband width is linear. The transmission bandwidth can be tuned by changing the solution concentration. The adjustable accuracy is 0.64318 nm -1·RIU -1 obtained after the detection of the transmission bandwidth at 1550 nm.