Abstract: F*-paracompactness in L-topological spaces was introduced. It was proved that F*-paracompactness has many good properties, such as that it is L-good extension, hereditary with respect to closed subsets,weakly in homeomorphic invariant property, and that the Cartesian product of a fuzzy compact space and a F*-paracompact space is a F*-paracompact space, as well as that a F*-paracompact Hausdorff space is both a S*-regular and a WS*-normal space. At last, a discussion about the relations of other paracompactnesses was given.

Key words: WS*-normality , S*-regularity, weakly induced space, F*-paracompactness, locally finite, L-topological space