ABSTRACT Molecular gas plays a critical role in explaining the quiescence of star formation (SF) in massive isolated spiral galaxies, which could be a result of either the low molecular gas content and/or the low SF efficiency. We present IRAM 30-m observations of the CO lines in the Sombrero galaxy (NGC 4594), the most massive spiral at $d\lesssim 30\rm ~Mpc$. We detect at least one of the three CO lines covered by our observations in all 13 observed positions located at the galactic nucleus and along an $\sim 25\rm ~kpc$-diameter dusty ring. The total extrapolated molecular gas mass of the galaxy is $M_{\rm H_2}\approx 4\times 10^{8}\rm ~M_\odot$. The measured maximum CO gas rotation velocity of $\approx 381\rm ~km~s^{-1}$ suggests that NGC 4594 locates in a dark matter halo with a mass $M_{\rm 200}\gtrsim 10^{13}\rm ~M_\odot$. Comparing to other galaxy samples, NGC 4594 is extremely gas poor and SF inactive, but the SF efficiency is apparently not inconsistent with that predicted by the Kennicutt–Schmidt law, so there is no evidence of enhanced SF quenching in this extremely massive spiral with a huge bulge. We also calculate the predicted gas supply rate from various sources to replenish the cold gas consumed in SF, and find that the galaxy must experience a starburst stage at high redshift, then the leftover or recycled gas provides SF fuels to maintain the gradual growth of the galactic disc at a gentle rate.