A hydrogen sensor with high sensitivity was demonstrated by coating the metal organic frameworks of ${\rm{UiO}}\! -\! {\rm{66 \!-\! N}}{{\rm{H}}_2}$ on an optical fiber Mach-Zehnder interferometer (MZI). The MZI was made of a fiber mismatch structure by using a core-offset fusion splicing method. The effective refractive index of the ${\rm{UiO}}\! -\! {\rm{66\! -\! N}}{{\rm{H}}_2}$ film varied with the absorption and release of hydrogen, and the interference resonant dip wavelength and the intensity of the MZI changed with the variations of the concentration of hydrogen. The experimental results showed that the proposed sensor had a high hydrogen sensitivity of 8.78 dB/% in the range from 0% to 0.8%, which is almost seven times higher than the existing similar hydrogen sensor.