A novel technique is proposed to fabricate a chirped fiber Bragg grating utilizing thermal diffusion of core dopant. The chirped grating is written with a uniform period by using UV exposure technique in the fiber whose effective index of the guided mode varies along its length. Thermal diffusion of the core dopant it employed to realize this change of the effective index. Through the thermal diffusion process, the effective index of the fiber decreases from its initial value. When the grating is written in the diffused core region, its reflection wavelength becomes shorter than that in the non-diffused region. The continuous change of effective index is required for making a chirped grating. The fiber is heated by a non-uniform heat source. When the uniform grating is written in this region, the reflection wavelength smoothly changes along the fiber length although the grating period is constant. By optimizing the fiber parameters to realize a highly chirped grating, we have obtained a typical one whose bandwidth is 14.1 nm at half maximum and maximum rejection in transmission is 29 dB. Additionally, the proposed method has an advantage to control the chirp profile with high mechanical reliability.