  The left-right twin Higgs model predicts one neutral Higgs boson $\phi_{0}$
and it acquires mass $m_{\phi_{0}}\sim \mu_{r}$ with the $\mu$ term, which can
be lighter than half the SM-like Higgs boson mass in a portion of parameter
space. Thus, the SM-like Higgs boson $h$ can dominantly decay into a pair of
light neutral Higgs bosons especially when $m_{h}$ is below the $WW$ threshold.
First, we examine the branching ratios of the SM-like Higgs boson decays and
find that the new decay mode $h\rightarrow \phi_{0}\phi_{0}$ is dominant for
the case of $m_{h}>2m_{\phi_{0}}$. Then we study the production via gluon
fusion followed by the decay into two photons or two weak gauge bosons and
found that the production rate can be significantly suppressed for some part of
parameter space. Finally, we comparatively study the process
$\gamma\gamma\rightarrow h \rightarrow b\bar{b}$ at ILC in the cases of
$m_{h}>2m_{\phi_{0}}$ and $m_{h}<2m_{\phi_{0}}$, respectively. We find that
these predictions can significantly deviated from the SM predictions, e.g., the
gluon-gluon fusion channel, in the cases of $m_{h}>2m_{\phi_{0}}$ and
$m_{h}<2m_{\phi_{0}}$, can be suppressed by about 80% and 45%, respectively.
Therefor, it is possible to probe the left-right twin Higgs model via these
Higgs boson production processes at the LHC experiment or in the future ILC
experiment.
