We present a novel optical fiber composed of a suspended core, a supporting ring and an outer ring. To establish a large holey region, a germanium-doped core is suspended by a silica ring and the entire structure is enclosed by another silica ring. By monitoring the Bragg wavelength shift of an FBG written in such a fiber with an air filling fraction of 65%, a hydrostatic pressure sensitivity of -43.6 pm/MPa was achieved experimentally. The high-pressure sensitivity is in good agreement with the numerically calculated value of ~40 pm/MPa. Due to the significant impact of the fiber core suspended in the large holey region inside the fiber, the pressure sensitivity improved by approximately eleven times compared to a Bragg grating inscribed in a standard single-mode fiber. To the best of our knowledge, it is the highest pressure sensitivity obtained for a FBG-based sensor experimentally, when compared to other FBG-based pressure sensors reported up to date. The large air hole region and the suspended core in the center of the fiber not only make the proposed fiber sensor a good candidate for pressure measurements, especially in the oil industry where space is at a premium, but also allow the detection of substances, by exploiting interaction of light with liquids or gases.