A hydrogen sulfide gas sensor based on Cu-deposited graphene-coated tapered Photonic Crystal Fiber (PCF) Mach-Zehnder Interferometer (MZI) was proposed and fabricated. The PCF-MZI was formed by fusion splicing a PCF with length of 45 mm which was sandwiched between two Single-Mode Fibers (SMF), and the air holes of PCF in the splicing regions were fully collapsed, and then it could motivate the cladding modes better. Using isopropanol as dispersion agent, the monolayer powders of graphene were added in the solution and fully dispersed, and then the PCF was dip-coated and sintered repeatedly. Cu-deposited graphene-coated PCF was used to make the sensor produce high sensitivity. The results show that with the increasing concentration of hydrogen sulfide, the output wavelengths appear blue shift, and a high hydrogen sulfide gas sensitivity of 0.042 03 nm/ppm and good linear relationship are obtained within a measurement range from 0 to 60 ppm for hydrogen sulfide gas. The system has the advantages of low cost, high sensitivity and simple structure, especially suitable for low concentration and on-line monitoring of hydrogen sulfide gas.