Short-period fiber Bragg gratings with weakly tilted grating planes generate multiple strong resonances in transmission. Our experimental results show that the wavelength separation between selected resonances allows the measurement of the refractive index of the medium surrounding the fiber for values between 1.25 and 1.44 with an accuracy approaching 1×10−4. The sensor element is 10  mm long and made from standard single-mode telecommunication grade optical fiber by ultraviolet light irradiation through a phase mask.