Grammar Induction could benefit from rich heterogeneous signals, such as text, vision, and acoustics. In the process, features from distinct modalities essentially serve complementary roles to each other. With such intuition, this work introduces a novel \emph{unsupervised visual-audio-text grammar induction} task (named \textbf{VAT-GI}), to induce the constituent grammar trees from parallel images, text, and speech inputs. Inspired by the fact that language grammar natively exists beyond the texts, we argue that the text has not to be the predominant modality in grammar induction. Thus we further introduce a \emph{textless} setting of VAT-GI, wherein the task solely relies on visual and auditory inputs. To approach the task, we propose a visual-audio-text inside-outside recursive autoencoder (\textbf{VaTiora}) framework, which leverages rich modal-specific and complementary features for effective grammar parsing. Besides, a more challenging benchmark data is constructed to assess the generalization ability of VAT-GI system. Experiments on two benchmark datasets demonstrate that our proposed VaTiora system is more effective in incorporating the various multimodal signals, and also presents new state-of-the-art performance of VAT-GI.