The key to multilingual grammar induction is to couple grammar parameters of different languages together by exploiting the similarity between languages. Previous work relies on linguistic phylogenetic knowledge to specify similarity between languages. In this work, we propose a novel universal grammar induction approach that represents language identities with continuous vectors and employs a neural network to predict grammar parameters based on the representation. Without any prior linguistic phylogenetic knowledge, we automatically capture similarity between languages with the vector representations and softly tie the grammar parameters of different languages. In our experiments, we apply our approach to 15 languages across 8 language families and subfamilies in the Universal Dependency Treebank dataset, and we observe substantial performance gain on average over monolingual and multilingual baselines.