  We have studied the dynamical fluctuation of net-charge of hadrons produced
in Au+Au collisions at energies that in near future will be available at the
Facility for Antiproton and Ion Research (FAIR). Data simulated by a
microscopic transport model based on ultra-relativistic quantum molecular
dynamics are analyzed for the purpose. The centrality and pseudorapidity
dependence of the net-charge fluctuation of hadrons are examined. Our simulated
results are compared with the results available for nucleus-nucleus collision
experiments held at similar energies. The gross features of our simulated
results on net-charge fluctuations are found to be consistent with the
experiment. At incident beam energy $E_{\rm lab}=10A$ GeV the magnitude of
net-charge fluctuation is very large, and in comparison with the rest its
centrality dependence appears to be a little unusual. The effect of global
charge conservation is expected to be very crucial at FAIR energies. The charge
fluctuations measured with varying pesudorapidity window size depend on the
collision centrality. The dependence is however exactly opposite in nature to
that observed in the Pb+Pb collision at $\sqrt{s_{_{NN}}}=2.76$ TeV.
