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 studied, emphasizing the contributions of the new physics induced by the new scalar and vector bosons of the BLHM: Si=H0,A0,ϕ0,η0,σ,H±,ϕ±,η±\documentclass[12pt]{minimal}
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\begin{document}$$S_i=H_0, A_0, \phi ^{0}, \eta ^{0}, \sigma , H^{\pm }, \phi ^{\pm }, \eta ^{\pm }$$\end{document}, and Vi=Z′,W′±\documentclass[12pt]{minimal}
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\begin{document}$$V_i=Z', W'^{\pm }$$\end{document} because these quantify the new physics. With these new contributions, we estimated bounds on 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.