  In the Littlest Higgs model, we comprehensively study the phenomenology of
the heavy photon A_H which is lightest, in most of the parameter space, among
newly introduced heavy gauge bosons and top-like vector quark. Unexpected
behavior is that lighter A_H suppresses the corrections to the electroweak
precision observables. For the global symmetry breaking scale f~3TeV, the heavy
photon can be light enough to be produced at the 500 GeV linear collider.
Through the calculation of the one-loop correction to the muon anomalous
magnetic moment, we show that even the light A_H with mass around 200 GeV
results in the negligible contribution. This is consistent with the current
inconclusive status of the theoretical calculation of the (g-2)_mu in the SM.
The effects of the Littlest Higgs model on the process e+ e- -> mu+ mu- are
also studied, which is one of the most efficient signals to probe the A_H.
