  In this paper, using the Bestest Little Higgs Model (BLHM) we calculate at
the one-loop level the contributions to the Anomalous Magnetic Dipole Moment
(AMDM) and Anomalous Weak Magnetic Dipole Moment (AWMDM) of the tau-lepton. The
implications from this model are study, emphasizing the contributions of the
new physics induced by the new scalar and vector bosons of the BLHM: $S_i=H_0,
A_0, \phi^{0}, \eta^{0}, \sigma, H^{\pm}, \phi^{\pm}, \eta^{\pm}$, and $V_i=Z',
W'$, because these quantify the new physics. With these new contributions we
estimated bounds on both the real and imaginary parts of the AMDM and AWMDM of
the tau-lepton. Our study complements other one-loop level research performed
on models beyond the Standard Model.
