Abstract We investigate the molecular gas properties of galaxies across the main sequence of star-forming (SF) galaxies in the local Universe using 12CO(J = 1–0), hereafter 12CO, and 13CO(J = 1–0), hereafter 13CO, mapping data of 147 nearby galaxies obtained in the COMING project, a legacy project of the Nobeyama Radio Observatory. In order to improve the signal-to-noise ratios of both lines, we stack all the pixels where 12CO emission is detected after aligning the line center expected from the first-moment map of 12CO. As a result, 13CO emission is successfully detected in 80 galaxies with a signal-to-noise ratio larger than three. The error-weighted mean of the integrated-intensity ratio of 12CO to 13CO lines (R1213) of the 80 galaxies is 10.9, with a standard deviation of 7.0. We find that (1) R1213 positively correlates to specific star-formation rate (sSFR) with a correlation coefficient of 0.46, and (2) both the flux ratio of IRAS 60 μm to 100 μm (f60/f100) and the inclination-corrected linewidth of 12CO stacked spectra ($σ _{{\rm ^{12}CO},i}$) also correlate with sSFR for galaxies with the R1213 measurement. Our results support the scenario where R1213 variation is mainly caused by changes in molecular gas properties such as temperature and turbulence. The consequent variation of the CO-to-H2 conversion factor across the SF main sequence is not large enough to completely extinguish the known correlations between sSFR and Mmol/Mstar (μmol) or star-formation efficiency (SFE) reported in previous studies, while this variation would strengthen (weaken) the sSFR–SFE (sSFR–μmol) correlation.