Novel oxidative dehydrogenation catalysts which are useful in vapor-phase oxidative dehydrogenation of lower alkanes with molecular oxygen to produce corresponding olefins at high yields are provided. The catalysts are characterized by containing Mn as the essential component and a crystal phase which is identified by the peaks appearing on their X-ray diffraction spectra (per Cu--K.alpha. cathode) where the diffraction angle 2.theta. (.+-.0.3.degree.) is at 32.9.degree., 55.2.degree., 23.1.degree., 38.2.degree. and 65.8.degree.. The use of those catalysts enables production of the olefins at high yields.