Provided is an alumina-based composite oxide having a large initial specific surface area and a small initial mean pore size, with excellent heat resistance of the specific surface area and pore volume; and a production method therefor. Specifically, provided is an alumina-based composite oxide wherein the initial crystallite diameter is 10 nm or less and the initial specific surface area is 80 m2/ml or more; after calcination at 1200° C. for 3 hours in air, the specific surface area is 10 m2/ml or more; the initial mean pore size is 10 nm or more and 50 nm or less; and after calcination at 1200° C. for 3 hours in air, the pore volume retention rate is 10% or more, which is determined by (P1/P0)×100 wherein P0 represents an initial pore volume (ml/g), and P1 represents a pore volume (ml/g) after calcination at 1200° C. for 3 hours in air.