We present the design and development of a novel tunable dispersion compensator with fixed center wavelength that is based on the electrical adjustment of the chirp of a fiber Bragg grating (FBG). Both temperature gradient and strain gradient are employed to adjust the chirp of the FBG jointly. The electrical current flowing through the taper on-fiber thin-film heater will introduce a temperature gradient on the FBG. The shrinkage of a negative thermal expansion coefficient (NTEC) ceramic due to the temperature rise will compress the tapered FBG mounted inside it, and this will introduce a strain gradient on the FBG. The center wavelength of the FBG will be kept fixed because the effect of temperature rise on the FBG and the effect of compression of the FBG will offset each other. Applying an electrical power of less than 0.68 W, we demonstrate a linearly chirped FBG whose dispersion can be continuously adjusted from -178 ps/nm to -302 ps/nm with a central wavelength shift of as small as 0.16 nm.