  We investigate the cosmological first-order chiral phase transition of QCD,
and for the first time calculate its parameters which can fully determine the
gravitational wave spectrum. With the state-of-the-art calculation from the
functional QCD method, we found that the large chemical potential of QCD phase
transition results in very weak and fast first-order phase transitions at the
temperature lower than $\mathcal{O}(10^2)$ MeV. These results further suggest
that the GW signals of NANOGrav are very unlikely sourced from the chiral phase
transition of QCD.
