In this paper, a novel optical fiber sensor based on an enlarged-taper tailored fiber Bragg grating (FBG) is proposed and experimentally demonstrated for the measurement of relative humidity. The enlarged-taper works as a multifunctional joint that not only excites cladding modes but also recouples the cladding modes reflected by the FBG back into the leading single mode fiber. Due to the fact that cladding modes have a strong evanescent field penetrating into the ambient medium, the intensity of the reflected cladding modes is greatly influenced by the refractive index (RI) of the ambient medium. Polyvinyl alcohol (PVA) film is plated on the fiber surface by dip-coating technique, as a humidity-to-refractive index transducer, whose RI variance from 1.49 to 1.34 when the ambient humidity increases from 20%RH to 95%RH. The relative humidity response of the sensing structure is investigated in our home-made humidity chamber with a commercial hygrometer. By monitoring the intensity of the reflected cladding modes, the RH variance can be demodulated. Experimental results show that RH sensitivity depends on the RH value, and a sensitivity up to 1.2 dB/%RH can be achieved within the RH range of 30-90%. A fast and reversible time response has also been investigated. Such a probe-type and reusable fiber-optic RH sensor is a very promising technology for biochemical sensing applications, e.g., breath analysis, chemical reaction monitoring.