This paper introduces deep syntactic structures to syntax-based Statistical Machine Translation (SMT). We use a Head-driven Phrase Structure Grammar (HPSG) parser to obtain the deep syntactic structures of a sentence, which include not only a fine-grained syntactic property description but also a semantic representation. Considering the abundant information included in the deep syntactic structures, it is interesting to investigate whether or not they improve the traditional syntax-based translation models basing on PCFG parsers. In order to use deep syntactic structures for SMT, this paper focuses on extracting tree-to-string translation rules from aligned HPSG tree-string pairs. The major challenge is to properly localize the non-local relations among nodes in an HPSG tree. To localize the semantic dependencies among words and phrases, which can be inherently non-local, a minimum covering tree is defined by taking a predicate word and its lexical/phrasal arguments as the frontier ...