  Extragalactic dispersion measures (DMs) obtained from observations of fast
radio bursts (FRBs) are an excellent tool for probing intergalactic medium
(IGM) and for conducting cosmography. However, the DM contribution from the IGM
(${\rm DM_{IGM}}$) depends on the fraction of baryon mass in the IGM, $f_{\rm
IGM}$, which is not properly constrained. As $f_{\rm IGM}(z)$ is geometrically
related to the Hubble parameter $H(z)$ and ${\rm DM_{IGM}}(z)$, here we propose
that combining two independent measurements of FRBs and $H(z)$ in similar
redshift ranges provides a novel and cosmology-free method to constrain the
evolution of $f_{\rm IGM}(z)$. Under the assumption that $f_{\rm IGM}$ is
evolving with redshift in a functional form, we forecast that the evolution of
$f_{\rm IGM}(z)$ can be well inferred in a combined analysis of $\sim3000$
${\rm DM_{IGM}}(z)$ derived from FRBs and $\sim50$ $H(z)$ derived from the
Hubble parameter data. Though the efficiency of our method is not as good as
that of the other model-independent method involving the joint measurements of
DM and luminosity distance of FRBs, our method offers a new model-independent
way to constrain $f_{\rm IGM}(z)$.
