  In this paper we study the production and decays of a light pseudoscalar
boson $\phi^0$ with $m_{\phi^0} \leq m_h/2$ appeared in the left-right twin
Higgs (LRTH) model, and explore its phenomenological consequences when the
latest LHC Higgs data are taken into account. We found that (a) the decay rate
$Br(h\to \phi^0\phi^0)$ can be as large as $80\%$ and can suppress
significantly the visible $\gamma\gamma$ signal rate, but the latest LHC Higgs
data put a strong constraint on it: $Br(h \to \phi^0\phi^0) \leq 30\%$ at
$3\sigma$ level; (b) the $p$-value of the LRTH model is around $0.6$, smaller
than that of the SM in most of the parameter space and approaches the SM value
$0.8$ for a sufficiently large $f$ parameter; (c) the neutral pseudoscalar
$\phi^0$ dominantly decay into $b\bar{b}$ and the decay rate $Br(\phi^0\to
b\bar{b})$ can be larger than $80\%$ for $m_{\phi^0}\leq 60$ GeV, and the
second main decay mode is $\phi^0\to \tau^{+}\tau^{-}$ with a branching ratio
about $14\%$; and (d) at the future $e^-e^+$ collider with $\sqrt{s}=250$ GeV,
the processes $e^{+}e^{-}\to Zh\to Z(\phi^0\phi^0)\to Z(4b,2b2\tau)$ are
promising for discovering such a light pseudoscalar $\phi^0$.
