  Primordial black holes (PBHs) can be both candidates of dark matter and
progenitors of binary black holes (BBHs) detected by the LIGO-Virgo-KAGRA
collaboration. Since PBHs could form in the very early Universe through the
gravitational collapse of primordial density perturbations, the population of
BBHs detected by gravitational waves encodes much information on primordial
curvature perturbation. In this work, we take a reliable and systematic
approach to reconstruct the power spectrum of the primordial curvature
perturbation from GWTC-3, under the hierarchical Bayesian inference framework,
by accounting for the measurement uncertainties and selection effects. In
addition to just considering the single PBH population model, we also report
the results considering the multi-population model, i.e., the mixed PBH and
astrophysical black hole binaries model. We find that the maximum amplitude of
the reconstructed power spectrum of primordial curvature perturbation can be
$\sim2.5\times10^{-2}$ at $\mathcal{O}(10^{5})~\rm Mpc^{-1}$ scales, which is
consistent with the PBH formation scenario from inflation at small scales.
