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A novel bandwidth-tuning method based on polymer-packaged fiber Bragg grating (FBG) is proposed and experimentally demonstrated. A FBG is embedded along the central axis in a polymer-filled rigid cylinder. The pressure-induced axial strain gradient along the FBG is calculated by using rigorous finite-element method (FEM). The corresponding broadening of the FBG reflection spectrum was numerically simulated using a transfer matrix method and experimentally analyzed. A linear spectral broadening up to 3.12 nm for a pressure of 0.8 MPa was observed.