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A systematic method of tunable dispersion compensation based on chirped fiber Bragg gratings (CFBGs) without a center wavelength shift will be proposed. The specially designed mechanical rotator can flexibly control the chirping ratio along the fiber gratings and consequently the group delay. The group delay can be linearly controllable since the proposed method can induce the linear strain gradient with the rotation angle change. The dispersion value can be effectively controlled in the range from -495.5 to -1406.0 ps/nm corresponding to the rotation angle. The resonant wavelength shift of CFBG is less than 0.03 nm over the dispersion tuning range. The theoretical analysis of the tuning mechanism based on the proposed method will also be discussed.