We argue that gamma-ray bursts (GRBs) may be the origin of the cosmic
gamma-ray background radiation observed in GeV range. It has theoretically been
discussed that protons may carry a much larger amount of energy than electrons
in GRBs, and this large energy can be radiated in TeV range by synchrotron
radiation of ultra-high-energy protons (\sim 10^{20} eV). The possible
detection of GRBs above 10 TeV suggested by the Tibet and HEGRA groups also
supports this idea. If this is the case, most of TeV gamma-rays from GRBs are
absorbed in intergalactic fields and eventually form GeV gamma-ray background,
whose flux is in good agreement with the recent observation.Comment: Accepted version by Astroparticle Physics, after some revision
