An efficient scheme to change the chirp rate of a fiber Bragg grating (FBG) has been developed based on a specially-designed cantilever beam with the beam-bending method. It allows, to date, the largest tuning range of 36 nm in reflection bandwidth of a chirped-FBG (CFBG) while keeping the center wavelength nearly fixed during the tuning process. Using this method, bandwidth-tunable fiber grating filters with tunable chromatic dispersion or differential group delay have been demonstrated. Channel spacing-tunable multi-wavelength filters based on both sampled- and superimposed-CFBGs have also been realized. Moreover, tuning of the bandwidth and channel spacing is continuous with this scheme that makes the achieved devices more flexible.