  High energy photons (>100 MeV) are detected by the Fermi/LAT from GRB 130427A
up to almost one day after the burst, with an extra hard spectral component
being discovered in the high-energy afterglow. We show that this hard spectral
component arises from afterglow synchrotron-self Compton emission. This
scenario can explain the origin of >10 GeV photons detected up to ~30000s after
the burst, which would be difficult to be explained by synchrotron radiation
due to the limited maximum synchrotron photon energy. The lower energy
multi-wavelength afterglow data can be fitted simultaneously by the afterglow
synchrotron emission. The implication of detecting the SSC emission for the
circumburst environment is discussed.
