Acrolein and acrylic acid are produced by vapor-phase catalytic oxidation of propylene in a multi-tubular, fixed-bed reaction vessel with the use of a composite oxide catalyst represented by the formula Mo.sub.a Bi.sub.b Fe.sub.c A.sub.d B.sub.e C.sub.f D.sub.g Si.sub.h O.sub.x, wherein A, B, C, and D represent components selectable from respective groups of elements, and the subscripts a through h and x are specific numbers of atoms of respective elements and groups of elements. This catalyst is adapted and packed in each reaction tube in a manner such that its activity is controlled to increase from the inlet toward the outlet of the tube.