An object of the present invention is to provide a catalyst support which can maintain the purifying ability of HC, CO and NO even after being exposed to a high temperature atmosphere such as about 1000° C. for a long term and a method which can easily produce the catalyst support. According to the present invention there is provided a method for producing a catalyst support of porous alumina formed with pores within which magneto-plumbite type complex oxide ((La.M) Al11O19 (wherein M is Mn or Fe)) is formed and a noble metal is supported on the magneto-plumbite type complex oxide comprising an aqueous solution preparing step for preparing aqueous solution containing lanthanum ions and either manganese ions or iron ions; an aqueous solution filling step for filling the pores of porous alumina with the aqueous solution obtained in the aqueous solution preparing step by a pore-filling method using the capillarity caused in the pores; a drying step for drying the porous alumina of which pores are filled with aqueous solution in the aqueous solution filling step, and a burning step for forming the magneto-plumbite type complex oxide by burning the porous alumina obtained in the drying step.