This investigation demonstrates leakage coupling between fundamental-mode and high-order mode resonance based on a periodical silica thin-film long-period grating (TFLPG) that was coated on a tapered fiber when wavelengths longer than the fundamental-mode cutoff were propagated. For the leaky guiding situation, these leakage modes still may exhibit strong mode coupling in the taper with the assistance of the TFLPG when the phase-matched condition is satisfied. An extremely high tuning efficiency of 62.9 nm/°C, which is equivalent to a measurement of sensitivity of approximately 168, 182 nm per refractive index unit, is achieved. To the best of our knowledge, this sensitivity is the highest achieved for a fiber sensor to date.