A simple and high sensitivity optical fiber relative humidity (RH) sensor based on Mach-Zehnder interferometer (MZI) is proposed and demonstrated in this paper. A single-mode fiber and a graded-index multimode fiber are connected by a fiber taper to form a section. Then an uncoated dispersion compensation fiber is sandwiched between two short sections of the graded-index multimode fiber.Therefore, a sensing structure is set up as a single-mode fiber-taper fiber-graded-index multimode fiber-dispersion compensation fiber-graded-index multimode fiber-taper laser-single-mode fiber. The taper fiber is used to augment the energy of the cladding mode. The two nodes of the graded-index multimode fiber can be looked as a mode coupler. Thus an MZI is constructed. Since the external RH change can make the transmission spectrum energy changed, we can obtain the RH by detecting the peak energy variation of the interference pattern induced by the evanescent-field interaction. The experimental results show that the peak energy changes linearly with surrounding relative humidity. Under the condition of 35%Rh-85%RH, the sensitivity of the sensor with a 20 mm dispersion compensation fiber is -0.0668 dB/%RH and the linearity is 0.995. Moreover, temperature response characteristics are investigated. Experimental results suggest that the transmission spectrum energy of the sensor is insensitive to temperature. With temperature increasing, the transmission spectrum presents obviously a red-shift, yet the peak energy of the monitoring point barely moves, which demonstrates its potential for measuring simultaneously RH and temperature. The proposed sensor has a small size and simple manufacturing process, which can make it widely used to measure RH.