  We study the merger rate of primordial black holes (PBHs) in self-interacting
dark matter (SIDM) halo models. To explore a numerical description for the
density profile of SIDM halo models, we use the result of a previously
performed simulation for SIDM halo models with $\sigma/m=10~{\rm
cm^{2}g^{-1}}$. We also propose a concentration-mass-time relation that can
explain the evolution of the halo density profile related to SIDM models.
Furthermore, we investigate the encounter condition of PBHs that may have been
randomly distributed in the medium of dark matter halos. Under these
assumptions, we calculate the merger rate of PBHs within each halo considering
SIDM halo models and compare the results with that obtained for cold dark
matter (CDM) halo models. To do this, we employ the definition of the time
after halo virialization as a function of halo mass. We indicate that SIDM halo
models for $f_{\rm PBH}>0.32$ can generate sufficient PBH mergers in such a way
that those exceed the one resulted from CDM halo models. By considering the
spherical-collapse halo mass function, we obtain similar results for the
cumulative merger rate of PBHs. Moreover, we calculate the redshift evolution
of the PBH total merger rate. To determine a constraint on the PBH abundance,
we study the merger rate of PBHs in terms of their fraction and masses and
compare those with the black hole merger rate estimated by the Advanced LIGO
(aLIGO)-Advanced Virgo (aVirgo) detectors during the third observing run. The
results demonstrate that within the context of SIDM halo models, the merger
rate of $10~M_{\odot}-10~M_{\odot}$ events can potentially fall within the
aLIGO-aVirgo window. We also estimate a relation between the fraction of PBHs
and their masses, which is well consistent with our findings.
