To efficiently obtain acrylic acid, maleic anhydride, (meth)acrylonitrile, etc., useful as a chemical raw material, etc., in high purity and yield by subjecting a hydrocarbon to vapor phase catalytic oxidation reaction by using a specific complex oxide catalyst.

A hydrocarbon is subjected to vapor phase catalytic oxidation reaction by using a complex oxide catalyst represented by the formula [X is Al, Si, Zr or Ti; Y is an alkali (earth) metal, Ni, Co, Zn, Ce, Mn, Ru, Pd, Pt, Sb, Te, B, In, La, P, Sn, Pb or Cu; Z is W, V, Nb or Ta; when (a) is 1, (b) is 1-20, (c) is 0.01-10, (d) is 0.001-20, (e) is 0-100, (f) is 0-10 and (g) 0-5; (n) is determined by oxidation state of other elements]. The vapor phase catalytic oxidation reaction is preferably ammoxidation reaction for obtaining α, β-unsaturated nitrile by oxidizing 3-6C alkane (e.g. propane) with ammonia in the presence of ammonia.