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We propose a new scheme for tunable dispersion using linearly chirped polymer optical fiber Bragg gratings made in fiber tapers. The simple tension and uniform heating to the fiber gratings act as the adjustment and control process. Dispersion is tuned by the applied tensile strain. Owing to the unusually large and negative thermooptic coefficient of polymer fiber, the center wavelength shift induced by the applied strain will be offset by the effect of the uniform heating, leading to the fixed center wavelength. Our simulation demonstrates a very large dispersion tuning range, say from 2400 to 110 ps/nm.