We propose a novel picture of the rotation mechanism of F-1-ATPase, a rotary-motor protein complex. Entropy, which originates from the translational displacement of water molecules, is treated as the key factor in the proposal. We calculate the water entropy gains upon formation of the alpha-beta, alpha-gamma, and beta-gamma subunit pairs. The gain is given as the difference between the hydration entropy of a subunit pair and the sum of the hydration entropies of the separate subunits forming the pair. The calculation is made using a hybrid of a statistical-mechanical theory for molecular liquids and morphometric approach. The water entropy gain is considered as a measure of tightness of the packing at each subunit interface. The results are highly correlated with the numbers of stable contacts at the subunit interfaces estimated by a molecular dynamics simulation. We also calculate the hydration entropies of three different subcomplexes comprising the gamma subunit, one of the beta subunits, and two a. subunits adjacent to them. The major finding is that the packing in F-1-ATPase is highly asymmetrical, and this asymmetry is ascribed to the water entropy effect. We discuss how the rotation of the gamma subunit is induced by such chemical processes as ATP binding, ATP hydrolysis, and release of the products. In our picture, the asymmetrical packing plays crucially important roles, and the rotation is driven by the water entropy effect.