Recent encoder-decoder approaches typically employ string decoders to convert images into serialized strings for image-to-markup. However, for tree-structured representational markup, string representations can hardly cope with the structural complexity. In this work, we first show via a set of toy problems that string decoders struggle to decode tree structures, especially as structural complexity increases. We then propose a tree-structured decoder that specifically aims at generating a tree-structured markup. Our decoders works sequentially, where at each step a child node and its parent node are simultaneously generated to form a sub-tree. This sub-tree is consequently used to construct the final tree structure in a recurrent manner. Key to the success of our tree decoder is twofold, (i) it strictly respects the parent-child relationship of trees, and (ii) it explicitly outputs trees as oppose to a linear string. Evaluated on both math formula recognition and chemical formula recognition, the proposed tree decoder is shown to greatly outperform strong string decoder baselines.