Two sets of items can share the same underlying conceptual structure, while appearing unrelated at a surface level. Humans excel at recognizing and using alignments between such underlying structures in many domains of cognition, most notably in analogical reasoning. Here we show that structural alignment reveals how different people's neural representations of word meaning are preserved across different languages, such that patterns of brain activation can be used to translate words from one language to another. Groups of Chinese and English speakers underwent fMRI scanning while reading words in their respective native languages. Simply by aligning structures representing the two groups' neural semantic spaces, we successfully infer all seven Chinese–English word translations. Beyond language translation, conceptual structural alignment underlies many aspects of high-level cognition, and this work opens the door to deriving many such alignments directly from neural representational content.