We present the first dynamic programming (DP) algorithm for shift-reduce constituency parsing, which extends the DP idea of Huang and Sagae (2010) to context-free grammars. To alleviate the propagation of errors from part-of-speech tagging, we also extend the parser to take a tag lattice instead of a fixed tag sequence. Experiments on both English and Chinese treebanks show that our DP parser significantly improves parsing quality over non-DP baselines, and achieves the best accuracies among empirical linear-time parsers.