Signal processing in optical frequency-domain reflectometry (OFDR) involves the cross correlation between the reference and the measured Rayleigh backscattering spectra (RBS), which is a time-consuming operation with a large data size. This work demonstrates a fast demodulation method to accelerate the data processing of OFDR in static strain measurement. The dispersion degree of the optical frequency-domain differential spectrum (OFDS) is analyzed to remove the strain-free RBS. Therefore, data demodulation can be accomplished based only on the local cross correlation (LCC) between the retained RBSs. The validity of the proposed method was verified by multiple sets of static strain experimental results. The time consumption of the proposed method is evaluated under the different sensing spatial resolutions and the number of padding zeros. Compared to the conventional method with the whole RBS, the proposed method decreases the time cost from 4575.7 to 637.1 ms when the fiber length is 40 m with 8-mm sensing spatial resolution and 6000 padding zeros.