The burned composite metal oxide of the present invention is a burned composite metal oxide which is porous and particulate and which is obtained by subjecting a slurry comprising at least one metal oxide (a), at least one metal compound (b) and a solvent to spray granulation to obtain granules, and burning the granules, the metal oxide (a) selected from the group consisting of a transition metal oxide and an oxide of a metal belonging to 3B, 4B and 5B of a periodic table, the metal compound (b) selected from the group consisting of an alkali metal compound and an alkali earth metal compound, wherein the metal oxide (a) and the metal compound (b) are sparingly soluble in the solvent; the burning is conducted after a heat-maintaining step of heating the granules obtained by the spray granulation at a temperature in a range of ±200° C. based on the decomposition temperature of the metal compound (b); and the metal compound (b) contains at least a nonmetallic element component desorbed in the heat-maintaining step.