A novel kind of wideband continuously tunable filtering phase shifter (FPS) working on switchable true time delay (TTD) or constant phase difference (CPD) mode is proposed. The FPSs are composed of external coupling networks (ECNs) and inner resonances. The ECNs are innovatively designed as real-to-complex impedance matching networks with independently tunable phase shift and phase slope. Additionally, a method for synthesizing the inner resonances with complex termination is presented. The systematic design method of the entire FPS is concluded. To validate the proposed method, a tunable FPS with bandwidth of 24%, phase shift range (PSR) of 90°, switchable phase modes, low phase error, and stable filtering performance is designed, fabricated and measured.