Abstract The Hubble parameter H(z) is directly related to the expansion of our universe. It can be used to study dark energy and constrain cosmology models. In this paper, we propose that H(z) can be measured using fast radio bursts (FRBs) with redshift measurements. We use dispersion measures contributed by the intergalactic medium, which is related to H(z), to measure the Hubble parameter. We find that 500 mocked FRBs with dispersion measures and redshift information can accurately measure Hubble parameters using Monte Carlo simulation. The maximum deviation of H(z) from the standard ΛCDM model is about 6% at redshift z = 2.4. We also test our method using Monte Carlo simulation. A Kolmogorov–Smirnov (K-S) test is used to check the simulation. The p-value of the K-S test is 0.23, which confirms internal consistency of the simulation. In the future, more localizations of FRBs make it an attractive cosmological probe.