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.
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