Efficiency is a prime concern in syntactic MT decoding, yet significant developments in statistical parsing with respect to asymptotic efficiency haven’t yet been explored in MT. Recently, McDonald et al. (2005b) formalized dependency parsing as a maximum spanning tree (MST) problem, which can be solved in quadratic time relative to the length of the sentence. They show that MST parsing is almost as accurate as cubic-time dependency parsing in the case of English, and that it is more accurate with free word order languages. This paper applies MST parsing to MT, and describes how it can be integrated into a phrase-based decoder to compute dependency language model scores. Our results show that augmenting a state-of-the-art phrase-based system with this dependency language model leads to significant improvements in TER (0.92%) and BLEU (0.45%) scores on five NIST Chinese-English evaluation test sets.