  The excessive dispersion measure (DM) of fast radio bursts (FRBs) has been
proposed to be a powerful tool to study intergalactic medium (IGM) and to
perform cosmography. One issue is that the fraction of baryons in the IGM,
$f_{\rm IGM}$, is not properly constrained. Here we propose a method of
estimating $f_{\rm IGM}$ using a putative sample of FRBs with the measurements
of both DM and luminosity distance $d_{\rm L}$. The latter can be obtained if
the FRB is associated with a distance indicator (e.g. a gamma-ray burst or a
gravitational wave event), or the redshift $z$ of the FRB is measured and
$d_{\rm L}$ at the corresponding $z$ is available from other distance
indicators (e.g. type Ia supernovae) at the same redshift. Since $d_{\rm
L}/{\rm DM}$ essentially does not depend on cosmological parameters, our method
can determine $f_{\rm IGM}$ independent of cosmological parameters. We
parameterize $f_{\rm IGM}$ as a function of redshift and model the DM
contribution from a host galaxy as a function of star formation rate. Assuming
$f_{\rm IGM}$ has a mild evolution with redshift with a functional form and by
means of Monte Carlo simulations, we show that an unbiased and
cosmology-independent estimate of the present value of $f_{\rm IGM}$ with a
$\sim 12\%$ uncertainty can be obtained with 50 joint measurements of $d_{\rm
L}$ and DM. In addition, such a method can also lead to a measurement of the
mean value of DM contributed from the local host galaxy.
