Graph-based and transition-based approaches to dependency parsing adopt very different views of the problem, each view having its own strengths and limitations. We study both approaches under the framework of beamsearch. By developing a graph-based and a transition-based dependency parser, we show that a beam-search decoder is a competitive choice for both methods. More importantly, we propose a beam-search-based parser that combines both graph-based and transitionbased parsing into a single system for training and decoding, showing that it outperforms both the pure graph-based and the pure transition-based parsers. Testing on the English and Chinese Penn Treebank data, the combined system gave state-of-the-art accuracies