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An S-tapered fiber sensor has been realized on the common single-mode fiber by a fusion splicer. The S fiber taper (SFT) can be considered as a compact fiber Mach-Zehnder interferometer with the total length of hundreds of microns. The spectral characteristics of the SFTs with different structure parameters including axial offsets and taper waist diameters have been studied. Sensing experiments have also been carried out to test their response to refractive index (RI) and axial strain. The SFT with an axial offset of 114 μm and a taper waist diameter of 54.6 μm exhibits the best combination property. Its RI sensitivity reaches as high as 2066 nm/RI unit in the RI range of 1.407-1.421 and the average strain sensitivity is -183.4 pm/με, which is the highest strain sensitivity, to the best of our knowledge, with one or two orders of magnitude larger than the existing fiber strain sensors.