A catalyst support for purification of exhaust gas comprising a porous composite metal oxide, the porous composite metal oxide containing alumina, ceria, and zirconia and having an alumina content ratio of from 5 to 80% by mass, wherein in the case where a noble metal is supported on the catalyst support, the porous composite metal oxide contains from 5 to 30% by mass of alumina, from 25 to 39% by mass of ceria, and from 33 to 51% by mass of zirconia, or in the case where a transition metal is supported on the catalyst support, the porous composite oxide contains from 30 to 80% by mass of alumina, and wherein the porous composite metal oxide is produced by: introducing independently a first raw material solution and a second raw material solution directly into a region in which a shear rate is from 1000 to 200000 sec -1, and homogeneously mixing the raw material solutions to obtain a colloidal solution of metal compounds, the first raw material solution containing an aluminum ion, a cerium ion, and a zirconium ion, and the second raw material solution containing a high-molecular dispersant having a weight average molecular weight of from 3000 to 15000, adjusting a pH of the colloidal solution to between 3 and 5, drying the colloidal solution after the pH adjustment or a suspension of metal compounds which is obtained by adding an organic amine to the colloidal solution after the pH adjustment in an oxidizing atmosphere under conditions of from 80 to 100°C and from 1 to 10 hours and then degreasing the colloidal solution or the suspension under conditions of from 200 to 400°C and from 1 to 5 hours, and then subjecting the solution or the suspension to heat treatment at from 700 to 1050°C in an oxidizing atmosphere, to obtain the porous composite metal oxide, and wherein after calcination in the air at 1100°C for 5 hours, the porous composite metal oxide satisfies a condition such that standard deviations of content ratios (as at% unit) of aluminum, cerium and zirconium elements are each 19 or less with respect to 100 minute areas (with one minute area being 300 nm in length × 330 nm in width) of the porous composite metal oxide, the standard deviation being determined by energy dispersive X-ray spectroscopy using a scanning transmission electron microscope equipped with a spherical aberration corrector. introducing independently a first raw material solution and a second raw material solution directly into a region in which a shear rate is from 1000 to 200000 sec -1, and homogeneously mixing the raw material solutions to obtain a colloidal solution of metal compounds, the first raw material solution containing an aluminum ion, a cerium ion, and a zirconium ion, and the second raw material solution containing a high-molecular dispersant having a weight average molecular weight of from 3000 to 15000, adjusting a pH of the colloidal solution to between 3 and 5, drying the colloidal solution after the pH adjustment or a suspension of metal compounds which is obtained by adding an organic amine to the colloidal solution after the pH adjustment in an oxidizing atmosphere under conditions of from 80 to 100°C and from 1 to 10 hours and then degreasing the colloidal solution or the suspension under conditions of from 200 to 400°C and from 1 to 5 hours, and then subjecting the solution or the suspension to heat treatment at from 700 to 1050°C in an oxidizing atmosphere, to obtain the porous composite metal oxide, and wherein after calcination in the air at 1100°C for 5 hours, the porous composite metal oxide satisfies a condition such that standard deviations of content ratios (as at% unit) of aluminum, cerium and zirconium elements are each 19 or less with respect to 100 minute areas (with one minute area being 300 nm in length × 330 nm in width) of the porous composite metal oxide, the standard deviation being determined by energy dispersive X-ray spectroscopy using a scanning transmission electron microscope equipped with a spherical aberration corrector.