We investigate the problem of efficiently incorporating high-order features into neural graph-based dependency parsing. Instead of explicitly extracting high-order features from intermediate parse trees, we develop a more powerful dependency tree node representation which captures high-order information concisely and efficiently. We use graph neural networks (GNNs) to learn the representations and discuss several new configurations of GNN{'}s updating and aggregation functions. Experiments on PTB show that our parser achieves the best UAS and LAS on PTB (96.0{%}, 94.3{%}) among systems without using any external resources.