  Pair production of Higgs boson at the Large Hadron Collider (LHC) is known to
be important for the determination of Higgs boson self-coupling and the probe
of new physics beyond the Standard Model (SM), especially the existence of new
fundamental scalar boson. In this paper we study in detail the Higgs pair
production at the LHC in a well-motivated model, the Gauged Two Higgs Doublet
Model (G2HDM) in which the two Higgs doublets are properly embedded into a
gauged $SU(2)_H$ and a dark matter candidate emerges naturally due to the gauge
symmetry. Besides the deviations of Higgs couplings from the SM predictions,
the existence of new scalars could enhance the production cross section of
Higgs boson pair at the LHC significantly. However, when we take into account
the relic density of dark matter and the null result in its direct search, only
moderate enhancement can be maintained. We also comment on the capability of
distinguishing the signal of a new generic scalar from the SM at the LHC,
assuming the Higgs pair production cross sections are the same.
