A three-filter-response switchable microwave photonic filters (MPF) based on micro-ring resonator (MRR) and fiber Bragg grating (FBG), using phase-intensity modulation, is proposed and experimentally demonstrated. By tuning the relative wavelengths of FBG reflectance spectrum, MRR notch, and optical carrier, the filter response of MPF can be switched between bandpass, flat-top bandpass, and high-pass. The bandpass, flat-top bandpass, and high-pass responses have bandwidth tuning ranges of 5.56-7.68 GHz, 6.23-11.92 GHz, and 5.83-10.86 GHz, respectively. Insertion loss of MRR under three responses is less than 10 dB. The switchable responses enable the proposed MPF to maintain higher flexibility, with a broad application such as frequency measurement and spurious suppression scenarios.