A single core-offset Mach-Zehnder interferometer (MZI) coated with polyvinyl alcohol (PVA) for simultaneous measurement of relative humidity (RH) and temperature is proposed in this paper. The sensing structure is fabricated by splicing dispersion compensating fiber (DCF) and no-core fiber (NCF) and splicing two single-mode fibers (SMF) at both ends, where the core-offset is located at the splicing of SMF and DCF. A part of the cladding of DCF is etched to excite the high-order cladding mode (LP10), and PVA is coated on the etched area. The refractive index of PVA varies due to the adsorption of water molecules. Therefore, when the ambient relative humidity and temperature change, the change of MZI phase difference causes the wavelength of the resonant dip to shift. The experimental results indicate that the proposed sensor has a sensitivity of 0.256 nm/RH% for RH range of 30%-95%, and a sensitivity of 0.153 nm/℃ for temperature range of 20℃-80℃, respectively. The simultaneous measurement of RH and temperature can be achieved by demodulating the sensitivity coefficient matrix. The proposed sensor has the characteristics of good repeatability, high sensitivity, and good stability, which make it potentially applications for the detection of RH and temperature measurement.