  The Fermi gamma-ray satellite has recently detected gamma-ray emissions from
radio galaxy cores. From these samples, we first examine the correlation
between the luminosities at 5 GHz, L_{5GHz}, and at 0.1-10 GeV, L_{gamma}, of
these gamma-ray loud radio galaxies. We find that the correlation is
significant with L_{gamma} \propto L_{5GHz}^{1.16} based on a partial
correlation analysis. Using this correlation and the radio luminosity function
(RLF) of radio galaxies, we further explore the contribution of gamma-ray loud
radio galaxies to the unresolved extragalactic gamma-ray background (EGRB). The
gamma-ray luminosity function is obtained by normalizing the RLF to reproduce
the source count distribution of the Fermi gamma-ray loud radio galaxies. We
find that gamma-ray loud radio galaxies will explain ~25% of the unresolved
Fermi EGRB flux above 100 MeV and will also make a significant contribution to
the EGRB in the 1-30 MeV energy band. Since blazars explain 22% of the EGRB
above 100 MeV, radio loud active galactic nuclei (AGNs) population explains
~47% of the unresolved EGRB. We further make an interpretation on the origin of
the EGRB. The observed EGRB spectrum at 0.2-100 GeV does not show an absorption
signature by the extragalactic background light. Thus, the dominant population
of the origin of EGRB at very high energy (>30 GeV) might be nearby gamma-ray
emitting sources or sources with very hard gamma-ray spectrum.
