  The evidence of the nano-Hertz stochastic gravitational wave (GW) background
is reported by multiple pulsar timing array collaborations. While a prominent
candidate of the origin is astrophysical from supermassive black hole binaries,
alternative models involving GWs induced by primordial curvature perturbations
can explain the inferred GW spectrum. Serendipitously, the nano-Hertz range
coincides with the Hubble scale during the cosmological quantum chromodynamics
(QCD) phase transition. The influence of the QCD phase transition can modify
the spectrum of induced GWs within the nano-Hertz frequency range,
necessitating careful analysis. We estimate GWs induced by power-law power
spectra of primordial curvature perturbations taking account of the QCD phase
transition. Then we translate the implication of the NANOGrav data into the
constraint on the power spectrum of the primordial curvature perturbation,
which suggests one would underestimate the amplitude by about $25\%$ and the
spectral index by up to $10\%$ if neglecting the QCD effect.
