The invention provides process for oxidative dehydrogenation of lower alkanes, by vapor phase oxidative dehydrogenation of C2-C5 lower alkanes in the presence of a catalyst and molecular oxygen to produce the corresponding olefins, in which the catalyst has a composition expressed by a general formula (1) below:in which A is at least one metal selected from the group consisting of molybdenum and chromium; Sb is antimony; W is tungsten; O is oxygen; and D is at least one metal selected from the group consisting of V, Nb, Ta, Fe, Co, Ni, Cu, Ag, Zn, B, Tl, Sn, Pb, Te, Li, Na, K, Rb, Cs, Mg, Ca, Sr, Ba, La, Ce and Sm; alpha, beta, gamma, delta and x denote atomic numbers of A, Sb, W, D and O, respectively, where when alpha=1, beta=0.5-10, gamma=0.1-10 and delta=0-3; and x is a numerical value determined by the state of oxidation of those elements other than oxygen.When these catalysts are used in reactions for oxidizing and dehydrogenating C2-C5 alkanes with molecular oxygen in vapor phase, corresponding olefins can be produced at high yield.