  Recent study of gamma rays originating from the region of galactic centre has
confirmed an anomalous $\gamma$-ray excess within the energy range 1-3 GeV.
This can be explained as the consequence of pair annihilation of a 31-40 GeV
dark matter into $b \bar b$ with thermal annihilation cross-section $\sigma v
\sim 1.4-2.0 \times 10^{-26}~\rm{cm^3/s}$. In this work we revisit the Inert
Doublet Model (IDM) in order to explain this gamma ray excess. Taking the
lightest inert particle (LIP) as a stable DM candidate we show that a 31-40 GeV
dark matter derived from IDM will fail to satisfy experimental limits on dark
matter direct detection cross-section obtained from ongoing direct detection
experiments and is also inconsistent with LHC findings. We show that a singlet
extended inert doublet model can easily explain the reported $\gamma$-ray
excess which is as well in agreement with Higgs search results at LHC and other
observed results like DM relic density and direct detection constraints.
