  The recently reported signal of common red noise between pulsars by several
pulsar timing array collaborations has been thought as evidence of the
stochastic gravitational wave background (SGWB) due to the Helling-Downs
correlation. In this study, we will search for the non-linearities of SGWB
through its effect on the overlap reduction function in NANOGrav 15-year data
set. In particular, we focus on a folded non-Gaussian component to SGWB whose
amplitude is quantified with a single parameter $\alpha$ in the unpolarized
case. The results reveal that such a non-Gaussianity of SGWB is favored, and
$\alpha=0$ (the Gaussian SGWB) is excluded at about $3\sigma$ level.
