The present invention provides a composite oxide for a high performance solid oxide fuel cell which can be fired at a relatively low temperature, and which has little heterogeneous phases of impurities other than the desired composition. The composite oxide is the one having a perovskite type crystal structure containing rare earth elements, and having constituent elements homogeneously dispersed therein. A homogeneous composite oxide having an abundance ratio of heterogeneous phases of at most 0.3% by average area ratio, and a melting point of at least 1470.degree. C., is obtained by using metal carbonates, oxides or hydroxides, and reacting them with citric acid in an aqueous system.