This paper presents a higher-order model for constituent parsing aimed at utilizing more local structural context to decide the score of a grammar rule instance in a parse tree. Experiments on English and Chinese treebanks confirm its advantage over its first-order version. It achieves its best F1 scores of 91.86% and 85.58 % on the two languages, respectively, and further pushes them to 92.80% and 85.60 % via combination with other highperformance parsers. 1