  As one of the promising candidates of cold dark matter (DM), primordial black
holes (PBHs) were formed due to the collapse of over-densed regions generated
by the enhanced curvature perturbations during the radiation-dominated era. The
enhanced curvature perturbations are expected to be non-Gaussian in some
relevant inflation models and hence the higher-order loop corrections to the
curvature power spectrum might be non-negligible as well as altering the
abundance of PBHs. In this paper, we calculate the one-loop correction to the
curvature power spectrum with local-type non-Gaussianities characterizing by
$F_{\mathrm{NL}}$ and $G_{\mathrm{NL}}$ standing for the quadratic and cubic
non-Gaussian parameters, respectively. Requiring that the one-loop correction
be subdominant, we find a perturbativity condition, namely
$|2cAF_{\mathrm{NL}}^2+6AG_{\mathrm{NL}}|\ll 1$, where $c$ is a constant
coefficient which can be explicitly calculated in the given model and $A$
denotes the variance of Gaussian part of enhanced curvature perturbation, and
such a perturbativity condition can provide a stringent constraint on the
relevant inflation models for the formation of PBHs.
