Abstract: A process for producing a composite oxide catalyst comprising at least Sb, Mo, V and/or Nb by the steps of combining and heating the sources of required respective elements, characterized in that a composite oxide represented by the following formula, which has been heated previously at a temperature of 600.degree. to 900.degree. C., is used as at least a part of a source of Sb supply:Sb.sub.p -X.sub.q -Y.sub.r,wherein x represents at least one selected from the group consisting of Ni, Fe, Co and Bi; Y represents at least one selected from the group consisting of Al and Si; p is a numeral of 1-40, q is a numeral of 1-20 and r is a numeral of 0-10, provided that when r is 0, Ni of X is at least partly supplied by nickel carbonate.A catalyst having a large mean pore size is obtained. When the catalyst is used in an oxidation reaction such as air oxidation of acrolein, acrylic acid as the object product can be obtained in high selectivity.