Most syntactic dependency parsing models may fall into one of two categories: transition- and graph-based models. The former models enjoy high inference efficiency with linear time complexity, but they rely on the stacking or re-ranking of partially-built parse trees to build a complete parse tree and are stuck with slower training for the necessity of dynamic oracle training. The latter, graph-based models, may boast better performance but are unfortunately marred by polynomial time inference. In this paper, we propose a novel parsing order objective, resulting in a novel dependency parsing model capable of both global (in sentence scope) feature extraction as in graph models and linear time inference as in transitional models. The proposed global greedy parser only uses two arc-building actions, left and right arcs, for projective parsing. When equipped with two extra non-projective arc-building actions, the proposed parser may also smoothly support non-projective parsing. Using multiple benchmark treebanks, including the Penn Treebank (PTB), the CoNLL-X treebanks, and the Universal Dependency Treebanks, we evaluate our parser and demonstrate that the proposed novel parser achieves good performance with faster training and decoding.