Dual-comb spectroscopy (DCS) is an emerging spectroscopic tool with the potential to simultaneously achieve a broad spectral coverage and ultrahigh spectral resolution with rapid data acquisition. However, the need for two independently stabilized ultrafast lasers significantly hampers the potential application of DCS. We demonstrate mode-resolved DCS in the THz region based on a free-running single-cavity dual-comb fiber laser with the adaptive sampling method. While the use of a free-running single-cavity dual-comb fiber laser eliminates the need for two mode-locked lasers and their frequency control, the adaptive sampling method strongly prevents the degradation of spectroscopic performance caused by the residual timing jitter in the free-running dual-comb laser. Doppler-limit-approaching absorption features with linewidths down to 25 MHz are investigated for low-pressure acetonitrile/air mixed gas by comb-mode-resolved THz spectroscopy. The successful demonstration clearly indicates its great potential for the realization of low-complexity, Doppler-limited THz spectroscopy instrumentation.