A relative humidity (RH) sensing scheme with high resolution and high interrogation speed based on an optoelectronic oscillator (OEO) is proposed and experimentally demonstrated. A carrier-suppression-effect-free single bandpass microwave photonic filter (MPF) with no baseband response is employed in the OEO to select the oscillating frequency, which is consisted of a non-coherent broadband optical source, a Mach-Zehnder interferometer (MZI) with one arm embedded a phase modulator, a dispersion compensation fiber and a photodetector. In one arm of the MZI, a section of optical fiber is coated with a polyvinyl alcohol (PVA) film acting as sensing probe, in which the PVA film can convert the RH variation to the strain on the fiber. When the RH changes, the arm-length difference and free spectral range of the MZI is changed, leading to a frequency change of the MPF as well as the oscillating signal of the OEO. By simply monitoring the frequency shift of the oscillating signal in the electrical domain, a high resolution and high interrogation speed RH measurement can be achieved. The temperature cross-sensitivity can be almost eliminated by adding a section of fiber without PVA film coating in the other arm of the MZI. An experiment is performed, and a high RH sensitivity of 2.016 MHz/%RH with a high resolution of 0.17 % is achieved.