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In the littlest Higgs model with T-parity (LHT),some new particles,such as the T-odd mirror quarks and goldstone bosons,can contribute to various observables.We calculate their contribution to Zc-c coupling.Some observables are related to Zc-c coupling,for example,the effective vector and axial-vector Zc-c coupling constants (gVc,gAc) and c-quark forward-backward asymmetry (AcFB).We give our predictions about gVc,gAc in the LHT model and show the allowed regions of the mirror quark masses based on the experimental data of gVc - gAc.Then,we present an explanation of AcFB.The littlest Higgs (LH) model[1] is an economical implementation of the little Higgs model[2,3] which was proposed as a possible approach to solve the little hierarchy problem.[4] It was soon realized that such a model suffers severe constraints due to the precision electroweak measurements.[5-8] The most serious constraints resulted from the tree-level contributions to the precision electroweak observables by the exchange of additional heavy gauge bosons in the theory.