A periodic density functional theory approach is used to investigate isolated monomeric Mo oxide species on γ-alumina. Eleven potential dioxo and monooxo Mo centers variously located on the (100) and (110) surfaces of γ-alumina are modeled. In these structures, the molybdenum is 2-, 3-, or 4-fold bonded to the surface. Thermodynamic stabilities of the Mo oxide species are compared for a wide range of temperatures, taking into account the hydration/dehydration state of the catalyst. It is predicted that in strict dehydrated conditions, square pyramidal monooxo species are dominant on the most exposed (110) surface of γ-alumina, while tetrahedral dioxo species and five-coordinate dioxo species are most probable on the minority (100) surface. The latter is the potential precursor of the most active sites for alkene metathesis. The presence of 4-fold coordinated monooxo Mo species, especially on the (100) facet, is also possible. At low water exposure, tetrahedral dioxo Mo species are present on both γ-alumina surfaces. It is also predicted that the Mo sites on the (110) γ-alumina are more stable than their analogues located on the (100) facet. A significant increase of the MoO stretching frequency is observed when going from the dioxo species to the monooxo structures on the majority (110) surface of γ-alumina. This agrees with the evolution of the Raman spectra upon calcinations. Such a frequency shift between the dioxo and the monooxo species does not happen on the minority (100) surface.