Adsorptions of methane, ethane and pentane on the γ-alumina (110C) surface are investigated with semi-empirical (PM3) cluster calculations. It is found that the abstraction of an H atom accompanied by the formation of a C-O bond is the most favorable reaction for methane on the alumina surface. For ethane- and pentane-alumina interactions, the abstraction of two H atoms accompanied by the formation of an alkene is the most favorable reaction. The surface Al atoms help to promote the reactions, but are not directly involved in the bond formation.