Based on Chinese dependency treebank PMT 1.0, the present study investigates the positional aspects of dependency distance (DD) quantitatively. Results show that (1) as the word position in the sentence increases, the tendency of mean dependency distance (MDD) in different sentence length groups shows striking similarity. The two longest MDDs generally are in the sentence-initial and sentence-final positions; (2) The consensus string (CS) and weighted consensus string (WCS) show some characteristics, which demonstrates again that human cognition plays an important role in affecting DD and dependency distance minimization is a universal tendency; (3) The distribution of DD in each sentential position can be captured by power law, which implies that something like a vertical structure of texts exists.