  We develop a low scale left-right symmetric model based on $SU(3)_C\times
SU(2)_L\times SU(2)_R\times U(1)_{B-L}\times Z_2$ with a simplified Higgs
sector consisting of only one bidoublet and one $SU(2)_R$ doublet. In this
model, the tiny values of light neutrino masses are generated through
Inverse-Seesaw mechanism. We emphasize that in this setup the tree-level Flavor
Changing Neutral Current can be strongly suppressed, consistent with the
current experimental constraints. We show that the lightest $CP$-even Higgs
boson, which is the SM-like Higgs, and the next-to-lightest Higgs $h'$, are
generated from the neutral components of the bidoublet. We emphasize that the
mass of the next-to-lightest Higgs boson can be of order few hundred GeVs. We
analyze the detection of $h'$ at the LHC for a center-of-mass energy of $14$
TeV and an integrated luminosity of $300$ ${\rm fb}^{-1}$ via di-Higgs channel:
$h'\to hh\to b\bar{b}\gamma\gamma$ and also in the $ZZ$ channel: $h'\to ZZ\to
4\ell$ at an integrated luminosity of $3000$ ${\rm fb}^{-1}$. We consider three
benchmark points for this analysis with $m_{h'}=250, 400$ and $600$ GeV. We
show that promising signals with good statistical significances can be obtained
in di-Higgs channel, with $2\gamma+2b$-jets final states.
