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The observations of high energy $\gamma$-ray emission from the Galacticcenter (GC) by HESS, and recently by Fermi, suggest the cosmic ray accelerationin the GC and possibly around the supermassive black hole. In this work wepropose a lepton-hadron hybrid model to explain simultaneously the GeV-TeV$\gamma$-ray emission. Both electrons and hadronic cosmic rays were acceleratedduring the past activity of the GC. Then these particles would diffuse outwardsand interact with the interstellar gas and background radiation field. Thecollisions between hadronic cosmic rays with gas is responsible to the TeV$\gamma$-ray emission detected by HESS. With fast cooling in the strongradiation field, the electrons would cool down and radiate GeV photons throughinverse Compton scattering off the soft background photons. This scenarioprovides a natural explanation of the observed GeV-TeV spectral shape of$\gamma$-rays.

Hybrid model of GeV-TeV gamma ray emission from Galactic Center