Sequence-to-sequence constituency parsing casts the tree structured prediction problem as a general sequential problem by top-down tree linearization,and thus it is very easy to train in parallel with distributed facilities. Despite its success, it relies on a probabilistic attention mechanism for a general purpose, which can not guarantee the selected context to be informative in the specific parsing scenario. Previous work introduced a deterministic attention to select the informative context for sequence-to-sequence parsing, but it is based on the bottom-up linearization even if it was observed that top-down linearization is better than bottom-up linearization for standard sequence-to-sequence constituency parsing. In this paper, we thereby extend the deterministic attention to directly conduct on the top-down tree linearization. Intensive experiments show that our parser delivers substantial improvements over the bottom-up linearization in accuracy, and it achieves 92.3 Fscore on the Penn English Treebank section 23 and 85.4 Fscore on the Penn Chinese Treebank test dataset, without reranking or semi-supervised training.