This paper presents the construction and evaluation of a deep syntactic parser based on Lexicalized Tree-Adjoining Grammars for the Vietnamese language. This is a complete sys- tem integrating necessary tools to process Vietnamese text, which permits to take as input raw texts and produce syntactic struc- tures. A dependency annotation scheme for Vietnamese and an algorithm for extracting dependency structures from derivation trees are also proposed. At present, this is the first Vietnamese parsing system capable of producing both constituency and dependency analyses with encouraging performances: 69.33% and 73.21% for constituency and dependency analysis accuracy, respectively.