We present a detailed analysis of the gamma-ray emission from HESS J1745-303 with the data obtained by the Fermi Gamma-ray Space Telescope in the first ~29 months observation.The source can be clearly detected at the level of ~18-sigma and ~6-sigma in 1-20 GeV and 10-20 GeV respectively. Different from the results obtained by the Compton Gamma-ray Observatory, we do not find any evidence of variability. Most of emission in 10-20 GeV is found to coincide with the region C of HESS J1745-303. A simple power-law is sufficient to describe the GeV spectrum with a photon index of ~2.6. The power-law spectrum inferred in the GeV regime can be connected to that of a particular spatial component of HESS J1745-303 in 1-10 TeV without any spectral break. These properties impose independent constraints for understanding the nature of this dark particle accelerator.
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