  The observation of diphoton excess around the mass of 750 GeV in LHC Run-II
motivates us to consider whether the singlet Higgs boson in the custodial Higgs
triplet model can serve as a good candidate because an earlier study of
comprehensive parameter scan shows that it can have the right mass in the
viable mass spectra. By assuming the singlet Higgs mass at 750 GeV, its total
width less than 50 GeV and imposing constraints from the LHC 8-TeV data, we
identify an approximately linear region on the $(v_\Delta, \alpha)$ plane along
which the exotic Higgs boson masses satisfy a specific hierarchy and have lower
possible spectra, where $v_\Delta$ denotes the triplet vacuum expectation value
and $\alpha$ is the mixing angle between the singlet Higgs boson and the
standard model-like Higgs boson. Although the diphoton decay rate can be
enhanced by charged Higgs bosons running in the loop in this region, it is
mostly orders of magnitude smaller than that required for the observed
production rate, except for the small $v_\Delta$ region when the diphoton
fusion production mechanism becomes dominant. Nonetheless, this part of
parameter space suffers from the problems of breakdown of perturbativity and
large uncertainties in the photon parton distribution function of proton.
