Carbons have been extensively investigated in recent years to explore their catalytic functions in oxidative dehydrogenations (ODH). Limited numbers of carbons have been directly compared under the same ODH condition, which makes their direct comparison impossible. This makes us difficult to understand a prime carbon design rule for simultaneously achieving high catalytic activity and stability. In this work, we investigated the catalytic properties of various carbons including an activated carbon, carbon nanotubes, onion-like carbons, and templated carbons in n-butane ODH. Regardless of the types of carbon structure, catalytic activities were linearly proportional to the number of quinone-type (C=O) functional groups, whereas the catalyst stability was correlated with the carbon oxidation stability. Because more C=O active sites are present in thermally unstable amorphous carbons, the carbon catalysts generally showed a trade-off between the catalytic activity and stability. However, a graphitic mesoporous carbon (CMK-3G) with the ‘coin-stacking’ of carbon layers showed high catalytic activity and stability simultaneously. This may be due to the fact that ‘coin-stacking’ of carbon layers allows a graphitic order of carbon framework as well as a large number of carbon edge sites where the C=O groups can be located.