In this work, we present a novel way of using neural network for graph-based dependency parsing, which fits the neural network into a simple probabilistic model and can be furthermore generalized to high-order parsing. Instead of the sparse features used in traditional methods, we utilize distributed dense feature representations for neural network, which give better feature representations. The proposed parsers are evaluated on English and Chinese Penn Treebanks. Compared to existing work, our parsers give competitive performance with much more efficient inference.