This paper proposes a novel microwave displacement sensor based on a filtering phase shifter (FPS), which can provide displacement sensing and intrinsic filtering functions simultaneously. The FPS comprises a third-order Chebyshev bandpass filter (BPF) network and a pair of transmission lines. With the derived closed-form formula of magnitude and phase response of the proposed FPS structure, variable insertion phase and constant filtering response characteristics are applied to design the linear displacement sensors for the first time. The displacement sensor mainly consists of double layers, where a pair of fixed transmission lines connect two ports in the first layer as a stator and an FPS structure in the second layer as a movable contact slider. The insertion phase drifts linearly along the displacement while the bandpass filtering response remains unchanged. A proof-of-concept microstrip sensor prototype operating at 2.98 GHz is implemented and tested to validate the proposed method experimentally. The measured results are in good agreement with the simulated ones, which shows that the proposed sensors can achieve an average phase sensitivity of about 12.8°/mm with a constant bandpass filtering response of 29.5% 3-dB (FBW).