This work presents an optically tunable chirped fiber Bragg grating (CFBG). The CFBG is obtained by a side-polished fiber Bragg grating (SPFBG) whose thickness of the residual cladding layer in the polished area (D(RC)) varies with position along the length of the grating, which is coated with a photoresponsive liquid crystal (LC) overlay. The reflection spectrum of the CFBG is tuned by refractive index (RI) modulation, which comes from the phase transition of the overlaid photoresponsive LC under ultraviolet (UV) light irradiation. The broadening in the reflection spectrum and corresponding shift in the central wavelength are observed with UV light irradiation density of 0.64mW/mm. During the phase transition of the photoresponsive LC, the RI increase of the overlaid LC leads to the change of the CFBG reflection spectrum and the change is reversible and repeatable. The optically tunable CFBGs have potential use in optical DWDM system and an all-fiber telecommunication system.