  Several groups have analyzed the publicly-available Fermi-LAT data and
reported a spatially extended $\gamma-$ray excess of around $1-3$ GeV from the
region surrounding the Galactic Center that might originate from annihilation
of dark matter particles with a rest mass $m_\chi \sim 30-40$ GeV. In this work
we examine the role of the diffuse Galactic gamma ray emission (DGE) templates
played in suppressing the GeV excess. For such a purpose, we adopt in total 128
background templates that have been generated by Ackermann et al.
\cite{FermiLAT:2012aa} in the study of the {Fermi-LAT} observations of the
diffuse gamma ray emission considering the effects of cosmic rays and the
interstellar medium. The possible GeV excess, assumed to follow the spatial
distribution of the prompt gamma-rays produced in the annihilation of dark
matter particles taking a generalized NFW profile with an inner slope
$\alpha=1.2$, has been analyzed in some regions of interest. The introduction
of such an additional component centered at the Galactic center is found to
have improved the goodness of fit to the data significantly in all background
template models regardless of whether the excess spectrum is fixed or not. Our
results thus suggest that the presence of a statistically significant GeV
excess in the inner Galaxy is robust thought its spectrum depends on the DGE
model adopted in the analysis. The possible physical origin of the GeV excess
component is discussed and in the dark matter model the annihilation cross
section of such particles is evaluated.
