Neural Machine Translation (NMT) based on the encoder-decoder architecture has recently achieved the state-of-the-art performance. Researchers have proven that extending word level attention to phrase level attention by incorporating source-side phrase structure can enhance the attention model and achieve promising improvement. However, word dependencies that can be crucial to correctly understand a source sentence are not always in a consecutive fashion (i.e. phrase structure), sometimes they can be in long distance. Phrase structures are not the best way to explicitly model long distance dependencies. In this paper we propose a simple but effective method to incorporate source-side long distance dependencies into NMT. Our method based on dependency trees enriches each source state with global dependency structures, which can better capture the inherent syntactic structure of source sentences. Experiments on Chinese-English and English-Japanese translation tasks show that our proposed method outperforms state-of-the-art SMT and NMT baselines.