The oxygen permeation properties of Sr4Fe6-xCoxO13 have been studied for 0 less than or equal to x less than or equal to 1.8. Samples with x > 1.5 consist of the perovskite phase SrFe1-xCoxO3-delta and the spinel phase Co3-xFexO4 in addition to the Sr4Fe6O13-type intergrowth phase. The total conductivity and the oxygen flux increase with increasing x. Although the oxygen flux in the undoped Sr4Fe6O13 remains constant, that in the x greater than or equal to 1.5 samples decreases upon cycling the permeation measurements. The decrease in oxygen flux on cycling is attributed to oxygen loss and changes in phase compositions at low oxygen partial pressures as indicated by thermogravimetric analysis.