We propose a corpus-based probabilistic framework to extract hidden common syntax across languages from non-parallel multilingual corpora in an unsupervised fashion. For this purpose, we assume a generative model for multilingual corpora, where each sentence is generated from a language dependent probabilistic contextfree grammar (PCFG), and these PCFGs are generated from a prior grammar that is common across languages. We also develop a variational method for efficient inference. Experiments on a non-parallel multilingual corpus of eleven languages demonstrate the feasibility of the proposed method.