  Primordial black holes (PBHs), as a potential macroscopic candidate for dark
matter, can encounter other compact objects in dark matter halos because of
their random distribution. Besides, the detection of gravitational waves (GWs)
related to the stellar-mass black hole-neutron star (BH-NS) mergers raises the
possibility that the BHs involved in such events may have a primordial origin.
In this work, we calculate the merger rate of PBH-NS binaries within the
framework of ellipsoidal-collapse dark matter halo models and compare it with
the corresponding results derived from spherical-collapse dark matter halo
models. Our results exhibit that ellipsoidal-collapse dark matter halo models
can potentially amplify the merger rate of PBH-NS binaries in such a way that
it is very close to the range estimated by the LIGO-Virgo observations. While
spherical-collapse dark matter halo models cannot justify PBH-NS merger events
as consistent results with the latest GW data reported by the LIGO-Virgo
collaboration. In addition, we calculate the merger rate of PBH-NS binaries as
a function of PBH mass and fraction within the context of ellipsoidal-collapse
dark matter halo models. The results indicate that PBH-NS merger events with
the mass of $(M_{PBH}\le 5 M_{\odot}, M_{NS}\simeq 1.4 M_{\odot})$ will be
consistent with the LIGO-Virgo observations if $f_{PBH}\simeq 1$. We also show
that to have at least on $(M_{PBH}\simeq 5 M_{\odot}, M_{NS}\simeq 1.4
M_{\odot})$ event in the comoving volume $1 Gpc^{3}$ annually,
ellipsoidal-collapse dark matter halo models constrain the abundance of PBHs as
$f_{PBH} \geq 0.1$.
