The generation mechanism of the laser beat frequency was studied by using chirped fiber Bragg grating as an example,and a model was established to realize the dispersion measurement of chirped fiber Bragg grating. The system structure and measuring principle are detailed demonstrated. The measurement results and the theoretical values are analyzed and compared,as a result, they are in good consistency. The accuracy of the dispersion measurement reaches to 0.1 ps at the spectrum analyzer resolution of 2.5 kHz. The dispersion measurement of chirped fiber Bragg grating confirms the feasibility of the system, at the same time, the system is relatively simple and highly accuracy. So it is expected to provide reference for the dispersion measurement.