Fast radio bursts (FRBs) are millisecond-duration radio transients and can be used as a cosmological probe. However, the dispersion measure (DM) contributed by the intergalactic medium (IGM) is hard to distinguish from other components. In this paper, we use the IllustrisTNG simulation to realistically estimate DMIGM up to z ∼ 9. We find pc cm−3 at z = 1. The probability distribution of DMIGM can be well fitted by a quasi-Gaussian function with a long tail. The tail is caused by structures along the line of sight in the IGM. Subtracting DM contributions from the Milky Way and host galaxy for localized FRBs, the DMIGM value is close to that given by the derived DMIGM–z relation. We also show the ability to constrain the cosmic reionization history with DMIGM of high-redshift FRBs in the IllustrisTNG universe. The derived DMIGM–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. DMIGM of high-redshift FRBs also provides an independent way to measure the optical depth of the cosmic microwave background. Our result can be used to derive the pseudo-redshifts of nonlocalized FRBs for DMIGM < 4000 pc cm−3.