  Through the relationship between dispersion measures (DM) and redshifts, fast
radio bursts (FRBs) are considered to be very promising cosmological probes. In
this paper, we attempted to use the DM-z relationship of FRBs to study the
helium abundance ($Y_{\rm He}$) in the universe. First, we used 17 current FRBs
with known redshifts for our study. Due to their low redshifts and the strong
degeneracy between $Y_{\rm He}$ and $\Omega_bh^2$, however, this catalog could
not provide a good constraint on the helium abundance. Then, we simulated 500
low redshift FRB mock data with $z\in[0,\,1.5]$ to forecast the constraining
ability on $Y_{\rm He}$. In order to break the degeneracy between $Y_{\rm He}$
and $\Omega_bh^2$ further, we introduced the shift parameters of the Planck
measurement $(R,l_A,\Omega_bh^2)$ as a prior, where $\Omega_bh^2$ represents
the baryon density parameter, and $R$ and $l_A$ correspond to the scaled
distance to recombination and the angular scale of the sound horizon at
recombination, respectively. We obtained the standard deviation for the helium
abundance: $\sigma({Y_{\rm He}}) = 0.025$. Finally, we considered 2000 higher
redshift FRB data with the redshift distribution of $[0,\,3]$ and found that
the constraining power for $Y_{\rm He}$ would be improved by more than 2 times,
$\sigma({Y_{\rm He}}) = 0.011$, which indicates that the FRB data with high
redshift can provide a better constraint on the helium abundance. Hopefully,
large FRB samples with high redshift from the Square Kilometre Array can
provide high-precision measurements of the helium abundance in the near future.
