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 μ → eγ decays, and the mass requirement of the right-handed neutrino ν R , the vector-like top partner T and the heavy gauge boson W H , m ν R > m T > m W H , are all considered in our calculation. Furthermore, since the neutral scalar φ 0 may be lighter than the 125 GeV Higgs, the direct searches from the h → φ 0 φ 0 channels can impose stringent upper limits on Br(h → φ 0 φ 0 ), which will reduce the allowed region of m φ 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 ≤ f ≤ 1100 GeV, 13 GeV ≤ m φ 0 ≤ 55 GeV, 100 GeV ≤ m φ ± ≤ 900 GeV, m ν R ≥ 15 TeV, and 200 GeV ≤ M ≤ 800 GeV, after imposing all the constraints mentioned above, where M here means the mass mixing coefficient Mq L q R , allowed by gauge invariance.