The structure and reactivity of Mo3S9 clusters, taken as a model for amorphous molybdenum trisulfide, have been investigated at the B3LYP density functional level of theory. Two computed ground-state cluster structures are close in energy and have similar structural parameters and vibrational modes. These values agree well with the available experimental data These cluster structures are considered to be formed simultaneously during the preparation process of catalysts. Their catalytic activity has been analyzed on the basis of frontier molecular orbital properties (FMO). It is mainly due to 4d-type orbitals of the unsaturated molybdenum centers without terminal sulfur coordination. The small HOMO-LUMO gaps suggest that Mo3S9 clusters can act as Lewis acids or Lewis bases.