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Pressure sensitivity and gas desorption time are two key parameters that determine the performance of pressure sensors. Polydimethylsiloxane (PDMS) film shows potential in highly sensitive pressure sensor, however the trade-off between high sensitivity and low desorption time presents a challenge. This article proposes a novel gas pressure sensor with ultra-high sensitivity and ultra-fast desorption based on a tapered fiber coated with Polydimethylsiloxane/Metal Organic Framework (PDMS/MOF) composite film. By doping a specific MOF with amino groups into PDMS, the gas adsorption capacity can be greatly enhanced. More importantly, the gas desorption time can be greatly reduced because the large pores in MOF create fast transport channels in PDMS. Experimental results show that the gas pressure sensitivity increases with an increase of MOF doping amount, leading to shorter gas desorption times. The sensor achieves a gas pressure sensitivity of up to −228.32 nm/MPa and a gas desorption time as short as 16 s within the pressure range of 0–100 KPa with doping amount of 5 wt%. A fiber Bragg grating is connected in series for compensation of temperature crosstalk. The proposed sensor provides a good reference for integrating porous materials and optical fibers in high-sensitivity gas and biochemical sensing applications.