A dual-comb spectroscopy (DCS) system uses two phase-locked optical frequency combs with a slight difference in the repetition frequency. The spectrum can be sampled in the optical frequency (OF) domain and reproduces the characteristics in the radio frequency (RF) domain through asynchronous optical sampling. Therefore, the DCS system shows great advantages in achieving precision spectral measurement. During application, the question of how to reserve the mutual coherence between the two combs is the key issue affecting the application of the DCS system. This paper focuses on a software algorithm used to realize the mutual coherence of the two combs. Therefore, a pair of free-running large anomalous dispersion fiber combs, with a center wavelength of approximately 1064 nm, was used. After the signal process, the absorption spectra of multiple species were simultaneously obtained (simulated using the reflective spectra of narrow-bandwidth fiber Bragg gratings, abbreviated as FBG). The signal-to-noise ratio (SNR) could reach 13.97 dB (25) during the 100 ms sampling time. In this study, the feasibility of the system was first verified through the simulation system; then, a principal demonstration experiment was successfully executed. The whole system was connected by the optical fiber without additional phase-locking equipment, showing promise as a potential solution for the low-cost and practical application of DCS systems.