Direct comb spectroscopy is a useful tool for obtaining highly accurate spectroscopic information. However, as the number of comb modes is very large and the optical energy is dispersed over them, the optical energy per each comb mode is ultrasmall, limiting the sensitivity of highly sensitive spectroscopy. If we can concentrate the optical energy into the comb modes that only overlap with the absorption spectra, we can demonstrate drastic improvements in its measurement sensitivity. In this study, we developed a freely controllable optical frequency comb source based on the spectral peak phenomenon. The comb modes overlapping the CH4 absorption spectra were transformed into background-suppressed spectral peaks at the nonlinear loop mirror using a CH4 gas cell. Coherence-preserving power scaling of the generated comb was demonstrated using a fiber Raman amplifier. Subsequently, only the single-comb mode was filtered using a newly developed spectral filter with an ultrahigh resolution. The maximum optical power of a single comb was estimated to be more than 10 mW. The ring-down decay signal from the high-finesse optical cavity was measured using a single selected mode of the generated controllable comb. As a demonstration, the 2v_3 bands of the CH4 absorption spectra were accurately measured by comb-mode-resolved, cavity ring-down spectroscopy (CRDS) with high sensitivity up to 4.2 x 10^(-11) cm^(-1). This sensitivity is two orders of magnitude higher than that of previously reported comb-based CRDS. The residual was only 0.29 %, indicating the high accuracy of the proposed spectrometer for molecular spectral analysis. This approach can be extended to other wavelength ranges and is useful for highly sensitive, high-resolution, comb-resolved spectroscopy.