  We report the results from our detailed analysis of the Fermi Large Area
Telescope (LAT) data for the pulsar binary PSR B1259-63/LS 2883. During the GeV
flares that occurred when the pulsar was in the periastron passages, we have
detected a 5--300 GeV component at $\simeq 5\sigma$ in emission from the
binary. The detection verifies the presence of the component that has been
marginally found in the previous studies of the binary. Furthermore, we have
discovered that this component was present even in the quiescent state of the
binary, specifically the mean anomaly phase 0.7--0.9. The component can be
described by a power law with photon index $\Gamma\sim 1.4$, and the flux in
the flares is approximately one order of magnitude higher than that in
quiescence. We discuss the origin of this component. It likely arises from the
inverse-Compton process: high-energy particles from the shock, due to the
interaction between the winds from the pulsar and massive companion, scatter
the seed photons from the companion to GeV/TeV energies. Based on this
scenario, model fits to the broad-band X-ray--to--TeV spectra of the binary in
the flaring and quiescent states are provided.
