We propose a method to suppress the beat noise generated in fiber low coherence interferometry (LCI) systems for characterizing the chromatic dispersion of chirped fiber Bragg gratings. The beat noise is considered as the dominant noise in the system because of the spectrum mismatch between interference arms due to the broad bandwidth of the light source and the introduction of dispersive components into the measurement arm, and is unfavorable for the signal quality. An experimental system is set up and interferograms of various situations are provided. Experiment results indicate that our method is feasible and effective, as it improves the signal to noise ratio effectively by a factor of more than 3, thereby expanding the measurement range of the LCI system.