Dual-phase membranes based on oxygen-ion-conducting doped ceria and electron-conducting lanthanum chromite show appreciable oxygen flux and good chemical compatibility between the two phases. In this work, Sm0.2Ce0.8O2−δ–La0.7Ca0.3CrO3−δ (volume ratio 60:40) composite membranes with different grain sizes are prepared. Membranes with large grains (1–5 μm) show much higher permeability than those with small grains (~ 300 nm). Applying a surface coating of a Sm0.2Ce0.8O2−δ–Sm0.5Sr0.5CoO3−δ catalyst reduces the running-in time from 220 to several hours and improves the steady-state permeability. The performance of the composite membrane is maintained when applying pure CO2 as sweep gas, showing promising potential in the application of these membranes in oxyfuel processes using CO2-diluted oxygen.