We will examine the muon g-2 anomaly with the background of the Higgs global fit data in the framework of the Left-Right Twin Higgs (LRTH) Models. The joint constrains of the precision electroweak data, the 125 GeV Higgs data, the leptonic flavor changing decay mu rightarrow egamma decays, and the mass requirement of the right-handed neutrino nu _R, the vector-like top partner T and the heavy gauge boson W_H, m_{nu _R}>m_T>m_{W_H}, are all considered in our calculation. Furthermore, since the neutral scalar phi ^0 may be lighter than the 125 GeV Higgs, the direct searches from the hrightarrow phi ^0phi ^0 channels can impose stringent upper limits on Br(hrightarrow phi ^0phi ^0), which will reduce the allowed region of m_{phi ^0} and f, the vacuum expectation value of the SM right-handed Higgs H_R. It is concluded that the muon g-2 anomaly can be explained in the region of 700 GeV le fle 1100 GeV, 13 GeV le m_{phi ^0}le 55 GeV, 100 GeV le m_{phi ^pm }le 900 GeV, m_{nu _R}ge 15 TeV, and 200 GeV le Mle 800 GeV, after imposing all the constraints mentioned above, where M here means the mass mixing coefficient M bar{q}_Lq_R, allowed by gauge invariance.