Recently, deep learning methods have achieved good results in dependency parsing for many natural languages. In this paper, we investigate the use of bidirectional long short-term memory network models for both transition-based and graph-based dependency parsing for the Vietnamese language. We also reportour contribution in building a Vietnamese dependency treebank whose tagset conforms to the Universal Dependency schema. Various experiments demonstrate the efficiency of this method, which achieves the best parsing accuracy in comparison to other existing approaches on the same corpus, with unlabeled attachment score of 84.45% or labeled attachment scoreof 78.56%.