  The observations of high energy $\gamma$-ray emission from the Galactic
center (GC) by HESS, and recently by Fermi, suggest the cosmic ray acceleration
in the GC and possibly around the supermassive black hole. In this work we
propose a lepton-hadron hybrid model to explain simultaneously the GeV-TeV
$\gamma$-ray emission. Both electrons and hadronic cosmic rays were accelerated
during the past activity of the GC. Then these particles would diffuse outwards
and interact with the interstellar gas and background radiation field. The
collisions between hadronic cosmic rays with gas is responsible to the TeV
$\gamma$-ray emission detected by HESS. With fast cooling in the strong
radiation field, the electrons would cool down and radiate GeV photons through
inverse Compton scattering off the soft background photons. This scenario
provides a natural explanation of the observed GeV-TeV spectral shape of
$\gamma$-rays.

High Energy Astrophysical Phenomena;High Energy Physics - Phenomenology