The reaction pathways and the energetics for the direct methane-methanol and benzene-phenol conversions that occur on the surface of Fe-ZSM-5 zeolite are analyzed from B3LYP DFT computations. We propose a reasonable model for "alpha-oxygen", a surface oxygen species responsible For the catalytic reactivities of Fe-ZSM-5 zeolite. Our model involves an iron-ore species on the AlO4 surface site of the zeolite as a catalytic active center and as a source of oxygen. The essential features of the reaction pathways for the methane-methanol and benzene-phenol conversions are identical, especially in bonding characters, In the initial stages of each reaction, methane or benzene comes into contact with the active iron site of the "alpha-oxygen" model, leading to the reactant (methane or benzene) complex. After the initial complex is formed, each reaction takes place in a two-step concerted manner, via neither radical species nor ionic intermediates. The concerted reaction pathway for the methane (benzene) hydroxylation involves an H atom abstraction and a methyl (phenyl) migration at the iron active center. From computed energetics for the reaction pathways, we predict that the benzene hydroxylation should be energetically more favorable than the methane hydroxylation.