Polymer optical fiber Bragg gratings (POFBGs) provide an efficient, robust, and cost-effective approach for humidity sensing. In this Letter, we propose and experimentally demonstrate a high-sensitivity and high-resolution POFBG-based humidity sensor that utilizes microwave photonic filtering response analysis. A POFBG and a silica FBG are used as the sensing probes, and a two-tap microwave photonic filter is developed to enable the high precision interrogation. Since only the poly (methyl methacrylate) (PMMA) based fiber is sensitive to humidity, the wavelength shift due to the humidity change is converted into the change of frequency response of the microwave photonic filter. A relationship between the humidity and the free spectral range (FSR) of the microwave photonic filter is established as the interrogation technique. Compared with the traditional approach by directly monitoring the wavelength shift using an optical spectrum analyzer, our proposed scheme can increase the humidity sensor resolution by two orders of magnitude, which greatly increases the accuracy of the humidity sensor, making it possible and feasible in many potential high-precision applications.