  Fast radio bursts (FRBs) are millisecond-duration radio transients and can be
used as a cosmological probe. However, the dispersion measure (DM) contributed
by intergalactic medium (IGM) is hard to be distinguished from other
components. In this paper, we use the IllustrisTNG simulation to realistically
estimate the $DM_{\rm IGM}$ up to $z\sim 9$. We find $DM_{\rm IGM} =
892^{+721}_{-270}$ pc cm$^{-3}$ at $z=1$. The probability distribution of
$DM_{\rm IGM}$ can be well fitted by a quasi-Gaussian function with a long
tail. The tail is caused by the structures along the line of sight in IGM.
Subtracting DM contributions from the Milky Way and host galaxy for localized
FRBs, the $DM_{\rm IGM}$ value is close to the derived $DM_{\rm IGM}-z$
relation. We also show the capability to constrain the cosmic reionization
history with the $DM_{\rm IGM}$ of high-redshift FRBs in the IllustrisTNG
universe. The derived $DM_{\rm IGM}-z$ relation at high redshifts can be well
fitted by a $tanh$ reionization model with the reionization redshift $z=5.95$,
which is compatible with the reionization model used by the IllustrisTNG
simulation. The $DM_{\rm IGM}$ of high-redshift FRBs also provides an
independent way to measure the optical depth of cosmic microwave background
(CMB). Our result can be used to derive the pseudo-redshifts of non-localized
FRBs for $DM_{\rm IGM}<4000$ \ \ pc cm$^{-3}$.
