  The stochastic gravitational wave background (SGWB) recently detected by the
PTA collaborations could be the gravitational waves (GWs) induced by curvature
perturbations. However, primordial black holes (PBHs) might be overproduced if
the SGWB is explained by the GWs induced by the curvature perturbations that
follow the Gaussian distribution. This motivates models associated with the
non-Gaussianity of the curvature perturbations that suppress the PBH production
rate. In this work, we show that the axion curvaton model can produce the
curvature perturbations that induce GWs for the detected SGWB while preventing
the PBH overproduction with the non-Gaussianity.
