  In this work we study the light Higgs scenario in the framework of two Higgs
doublet model (2HDM). In this case the heavier CP-even Higgs boson $H$ in 2HDM
is the SM-like Higgs with 125 GeV mass and a CP-even Higgs boson $h$ lighter
than 125 GeV exhibits in the spectrum. We find that this scenario exists in the
alignment limit of $\sin(\beta-\alpha)\simeq 0$ and is still allowed by the
global fit of the 125 GeV Higgs and the direct searches for $H\to hh$ and $h\to
\gamma\gamma$. The case of $M_h<M_H/2$ is highly constrained as the exotic
decay mode $H\to hh$ is kinematically allowed. We focus on the $M_h>M_H/2$ case
and simulate the pair production of the light Higgs boson at the LHC. The pair
production is sensitive to the soft $\mathbb{Z}_2$ symmetry breaking term
$m_{12}$ in the 2HDM potential through the Higgs self-couplings. We find that
the future high-luminosity LHC can discover the $b\bar{b}\gamma\gamma$ signal
in the region of $\tan\beta\lesssim 1$ and $0<m_{12}<100$ GeV allowed by the
theoretical constraints.
