  The recent report of NANOGrav is gathering attention since its signal can be
explained by the stochastic gravitational waves (GWs) with $\Omega_{\rm GW}\sim
10^{-9}$ at $f\sim 10^{-8}$Hz. The PBH formation scenario is one of the
candidates for the NANOGrav signal, which can simultaneously explain the
observed $30 M_\odot$ black holes in the binary merger events in LIGO-Virgo
collaboration. We focus on the type II axion-like curvaton model of the PBH
formation. In type II model the complex field whose phase part is the axion
rolls down from the origin of the potential. It is found that type II model
achieves the broad power spectrum of the density perturbations and can
simultaneously explain the LIGO-Virgo events and the NANOGrav signal. We also
improve the treatment of the non-Gaussianity of perturbations in our model to
estimate the amplitude of the induced GWs precisely.
