There are urgent demands of ultraviolet (UV) photodetectors with high sensitivity and fast response due to the wide application of ultraviolet light in the fields of medical treatment, space exploration, optical communication and semiconductor industry. The response speed of traditional ZnO-based UV photodetectors is always limited by the carrier mobility and electrical resistance caused by the external circuits. Utilizing the all-optical detection method may replace the complex circuit structure and effectively improve the response speed of photodetectors. Here, a fast-response fiber-optic UV photodetector is proposed, where a ZnO micro-pillar is fixed on the end face of a fiber-tip and acts as a Fabry-Pérot interferometer (FPI). Under the irradiation of UV light, the photo-generated carriers change the refractive index of the ZnO micro-pillar, leading to a redshift of the interference wavelengths of the ZnO FPI. To enhance this effect, a discontinuous Ag film with an island-like structure is coated on the surface of ZnO micro-pillars through magnetron sputtering, and therefore the sensitivity of the proposed device achieves to 1.13 nm/(W·cm-2), which is 3.9 times higher than that of without Ag-decoration, due to the intensification of photo-carrier change with the help of the Schottky junction formed between Ag film and ZnO micro-pillar. Meanwhile, since the response speed of the proposed device is mainly determined by the temporal RI change of ZnO micro-pillar, the fiber-optic UV photodetector also shows very fast response with a rise time of 35 ns and a decay time of 40 µs. The demonstrated structure takes full advantage of optical fiber devices, exhibiting compactness, flexibility, fast response and immune to electromagnetic interference, which paves a new way for the next generation of photodetection devices.