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The scalar-induced gravitational waves (SIGW), arising from large amplitudeprimordial density fluctuations, provide a unique observational test fordirectly probing the epoch of inflation. In this work, we provide constraintson the SIGW background by taking into account the non-Gaussianity in theprimordial density fluctuations, using the third observing run (O3) data of theLIGO-Virgo-KAGRA collaboration. We find that the non-Gaussianity gives anon-negligible effect on the GW energy density spectrum and starts to affectthe analysis of the O3 data when the non-Gaussianity parameter is $F_{\rm NL} >3.55$. Furthermore, the constraints exhibit asymptotic behavior given by$F_{\rm NL} A_g = \rm{const.}$ at large $F_{\rm NL}$ limit, where $A_g$ denotesthe amplitude of the curvature perturbations. In the limit of large $F_{\rmNL}$, we placed a 95% confidence level upper limit $F_{\rm NL} A_g \leq 0.13,0.09, 0.10$ at fixed scales of $10^{16}, 10^{16.5}, 10^{17}~{\rm Mpc}^{-1}$,respectively.

Constraints on Non-Gaussian primordial curvature perturbation from the LIGO-Virgo-KAGRA third observing run