The present invention provides a porous composite oxide comprising an aggregate of secondary particles in the form of aggregates of primary particles of a composite oxide containing two or more types of metal elements, and having mesopores having a pore diameter of 2-100 nm between the secondary particles; wherein, the percentage of the mesopores between the secondary particles having a diameter of 10 nm or more is 10% or more of the total mesopore volume after firing for 5 hours at 600.degree. C. in an oxygen atmosphere.