According to the temperature tunability of chirped fiber grating, a new kind of dispersion compensation method was proposed, which make chirp fiber grating in a continuous linear temperature gradient field. The dispersion of chirped fiber Bragg grating is fine-tuned by adjusting temperature difference between the ends of the fiber Bragg grating. The dispersion mismatch in chirped pulse amplification system, which is based on the chirped fiber Bragg grating as pulse stretcher and chirped volume Bragg grating as pulse compressor, can be continuously compensated, and the feasibility of this method is verified by experiment. The experimental results show that the application fields, when the temperature difference of the continuous temperature gradient along the chirped fiber Bragg grating continuously changes from 0℃ to 50℃, the dispersion mismatch between the stretcher and compressor can be continuously adjusted, thereby eliminating the tedious pulse width optimization steps. The gradient of the continuous linear temperature field is reported for the first time to fine-tune the dispersion mismatch in chirped pulse amplification system that uses the chirped fiber Bragg grating as pulse stretcher and chirped volume Bragg grating as pulse compressor.