The Sr(Fe0.5Nb0.5)O3 (SFN) dense ceramics were sintered at 1450°C in N2, air and O2 atmosphere for 3 h, respectively. All ceramics sintered at various atmospheres exhibited a single phase with perovskite structure in the space group Pmm(221). The microstructure and dielectric properties of SFN ceramics were related to the sintering atmospheres. The dielectric constant of the sample sintered in N2 atmosphere reached the highest value (about 23,000) at room temperature. With the increasing of the oxygen partial pressure, the dielectric constant decreased significantly. Moreover, the complex plane impedance plots even demonstrated that the samples were electrically heterogeneous and consisted of low resistive grains and high resistive grain boundaries. The giant dielectric phenomenon of SFN ceramics was therefore attributed to the IBLC model. The resistivity of grain boundary increased drastically with increasing the oxygen concentration while the resistivity of grain increased inconspicuously. With XPS analysis, it was illustrated that the oxygen vacancy concentrations of SFN ceramics decreased with increasing oxygen concentration, which indicated that a higher value of dielectric constant of SFN ceramics was obtained at lower oxygen concentration. The results strongly indicated that further improvement of the dielectric characteristics in the present ceramics is expected by optimizing sintering atmospheres.