The littlest Higgs(LH) model is a very interesting extension of the standard model(SM). It can be an alternative candidate of new physics beyond the SM which solves the hierarchy problem. The LH model predicts a set of new particles, such as heavy gauge bosons (AH, ZH,WH), heavy vector-like quark (T), and modifies the SM-like gauge boson couplings to the other SM-like particles. In this thesis we have performed phenomenological investigation of the quantum effects of the Littlest Higgs Model in two fields. One is the LH model quantum effects in the top quark rare decays t → cH0, and another item is the calculation of the anomalous magnetic moment of Muon in the LH model. In the study of the decay width of the top quark rare decay channel t → cH0 in the LH model, we conclude that the branch ratio of this rare decay is sensitive to some of the LH model parameters, such as the LH model parameter x, Higgs boson mass mH0 and symmetry breaking energy scale f in some parameter space from our numerical results, but relatively insensitive to the value of the cosine of the mixing angle c and the ratio λ1/λ2 in our chosen parameter space. The decay branch ratio of the t → cH0 process in the LH model is at most of order 10-12 and is generally dozens times larger than that in the SM. We find also that the ratio of branch ratio BrLH and BrsM is largely enhanced, when the parameter x goes very close to one and the value of scale f is relative small. We calculated also the muon anomalous magnetic moment including all the one-loop weak contributions in the LH model, and adopted the recent best results of QED and hadronic contributions. We find that in the electroweak precision data preferring parameter space, the LH model weak contribution can slightly reduce the discrepancy of the muon anomalous magnetic moment between the experimental result and the theoretical prediction, comparing with in the SM case. The typical deviation value in the LH model △aμ= aμExp-aμLH is about 22.5 × 10-10, which is 4％ smaller than △aμ= aμExp - aμSM We conclude that the LH model could give a relative small, but non-negligible extra weak contribution to the aμ, and could reduce the deviation of △aμ from 2.6σ for the SM to 2.5σ for the LH model.