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We report the fabrication and characterization of a highly sensitive refractive-index sensor based on a long-period grating (LPG) pair with a fiber-taper section in between. Two LPGs with ∼3-dB transmissivity form an in-fiber Mach-Zehnder interferometer. A fiber taper is made between the two LPGs to improve and tailor the sensitivity of the sensor. Enhanced sensitivity, which is about five times higher than that of a normal LPG pair, is achieved in the experiment.