We propose a strain fiber sensor that is interrogated via longitudinal mode beat frequency with a linear chirped fiber Bragg grating (CFBG). Unlike conventional sensors, in the proposed sensor, the CFBG is used to convert wavelength changes into resonant cavity length changes. Further, the beat frequency stability of the fiber laser is fully utilized to significantly improve measurement accuracy. Consequently, because cavity changes account for 5.1% of the total cavity length, the measurement accuracy can be as large as 7.06×10−7 ϵ—i.e., approximately five times greater than the accuracy obtained by stretching the resonant cavity fiber. The maximum experimental strain error range is ±14.5 μϵ.