In this paper a bidirectional parser for Lexicalized Tree Adjoining Grammars will be presented. The algorithm takes advantage of a peculiar characteristic of Lexicalized TAGs, i.e. that each elementary tree is associated with a lexical item, called its anchor. The algorithm employs a mixed strategy: it works bottom-up from the lexical anchors and then expands (partial) analyses making top-down predictions. Even if such an algorithm does not improve the worst-case time bounds of already known TAGs parsing methods, it could be relevant from the perspective of linguistic information processing, because it employs lexical information in a more direct way.