A method of synthesizing metal composite oxide, the method including: a step of separately introducing into a high-speed stirring apparatus a ceria composite oxide microparticle colloid having a mean particle diameter of 10 nm or less after adding a dispersant and an alumina microparticle colloid having a mean particle diameter of 10 nm or less after adding a dispersant; a step of synthesizing alumina-ceria composite oxide microparticles by allowing the ceria composite oxide microparticles and the alumina microparticles that have been introduced into the high-speed stirring apparatus to react in a microscopic space; and a step of applying a shearing force of 17000 sec−1 or more to the alumina-ceria composite oxide microparticles.