  The radiative Higgs decays h -> gamma l+l- with l=e,mu and tau are analyzed
in the standard model using m_h=125 GeV. Both tree and one-loop diagrams for
the processes are evaluated. In addition to their decay rates and dilepton
invariant mass distributions, we focus on the forward-back asymmetries in these
modes. Our calculation shows that the forward-backward asymmetries in h ->
gamma e+e- and h -> gamma mu+mu- could be up to 10^{-2} while in the tau+tau-
final state, these asymmetries are below 1%. Thus the forward-backward
asymmetries in h -> gamma l+l- might be interesting observables in the future
precise experiments both to test our understanding of Higgs physics in the
standard model and to probe the novel Higgs dynamics in new physics scenarios.
