  We investigate the dispersion measure(DM) and scattering of FRBs by the
intergalactic-medium(IGM), foreground and host halos, using cosmological
hydrodynamical simulation. We find that the median DM caused by foreground
halos is around 30\% of that caused by the IGM, but has a much larger variance.
The DM induced by hosts deviates from a log-normal distribution, but exhibits
an extended distribution in the range of $1-3000 \ {\rm{pc\, cm^{-3}}}$ with a
median value $\sim 100 \ {\rm{pc\, cm^{-3}}}$. Then we produce mock FRB
sources, assuming a uniform distribution in the range $z\sim 0-0.82$, to
consider the propagation effect of IGM, foreground and host halos on FRB
signals simultaneously. The DM distribution of mock sources agrees well with
the observation. The fitted DM-redshift relation of the mock sources can
provide a rough estimation of the redshifts of observed events with errors
$\delta z \lesssim 0.15$. The distribution of mock sources in the DM-scattering
time($\tau$) space can also match the observation, assuming a Kolmogorov
turbulence model with the inner and outer scale is 1000 km to 1 AU, and 0.2-10
pc respectively. Finally, we estimate the relative importance of these medium
on DM and $\tau$ in our models. The IGM and host halos are the primary and
secondary sources to the extragalactic DM, $\rm{DM_{exg}}$. Meanwhile, the
contribution from foreground halos increases as $\rm{DM_{exg}}$ increases. The
host and foreground halos may be the most important medium for scattering.
Statistically, the latter may dominate the scattering of events with
$\rm{DM_{exg}} \gtrsim 200 \ {\rm{pc\, cm^{-3}}}$.
