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 beam-search. 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 transition-based 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 of 92.1% and 86.2%, respectively.