  From the total cross section for the reaction $e^+e^-\to \tau^+\tau^-\gamma$
at the $Z_1$ pole and in the framework of a simplest little Higgs model (SLHM),
we get a limit on the characteristic energy scale of the model $f$, $f \geq
5.4$ $TeV$, which in turn induces bounds on the electromagnetic and weak dipole
moments of the tau-lepton. Our bounds on the electromagnetic moments are
consistent with the bounds obtained by the L3 and OPAL collaborations for the
reaction $e^+e^-\to \tau^+\tau^-\gamma$. We also obtained bounds on the tau
weak dipole moments which are consistent with the bounds obtained recently by
the DELPHI and ALEPH collaborations from the reaction $e^+e^-\to \tau^+\tau^-$.
