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A narrow-band apodized fiber Bragg grating was fabricated with a phase mask method that incorporated a fluorescence monitoring technique. The grating length was 100 mm and the 3-dB reduced bandwidth was as small as 0.04 nm. The 20-dB reduced bandwidth was 0.1 nm at a center wavelength of 1554 mm. A single longitudinal oscillation mode of a 10-GHz pulse train from a mode-locked fiber laser was successfully extracted using the grating.