  We will examine the Left-Right Twin Higgs(LRTH) Models as a solution of muon
g-2 anomaly with the background of the Higgs global fit data. In the
calculation, the joint constrains from the theory, the precision electroweak
data, the 125 GeV Higgs data, the leptonic flavor changing decay \mu \to
e\gamma decays, and the constraints m_{\nu_R}>m_T>m_{W_H} are all considered.
And with the small mass of the \phi^0, the direct searches from the $h\to
\phi^0\phi^0$ channels can impose stringent upper limits on Br(h\to
\phi^0\phi^0) and can reduce the allowed region of m_{\phi^0} and f. It is
concluded that the muon g-2 anomaly can be explained in the region of 200 GeV
\leq M\leq 500 GeV, 700 GeV \leq f\leq 1100 GeV, 13 GeV \leq m_{\phi^0}\leq 55
GeV, 100 GeV \leq m_{\phi^\pm}\leq 900 GeV, and m_{\nu_R}\geq 15 TeV after
imposing all the constraints mentioned above.
