Combining the characteristics of linear chirped fiber Bragg grating (CFBG), a stress fiber sensor based on laser beat frequency is designed. Using the method of CFBG converting the wavelength change into the length change of resonant cavity, the wavelength demodulation is achieved. The proposed method is different from previous methods changing the cavity length. The group delay of linear CFBG is measured and the system structure and principle are described in detail. Besides, the measuremental results and precision are analyzed and calculated. The length change of cavity can reach 6.2 cm, which accounts for 2.55% of total cavity length. The results show that the strain measurement precision can be up to 10-7 N.