Modern approaches to Constituency Parsing are mono-lingual supervised approaches which require large amount of labelled data to be trained on, thus limiting their utility to only a handful of high-resource languages. To address this issue of data-sparsity for low-resource languages we propose Universal Recurrent Neural Network Grammars (UniRNNG) which is a multi-lingual variant of the popular Recurrent Neural Network Grammars (RNNG) model for constituency parsing. UniRNNG involves Cross-lingual Transfer Learning for Constituency Parsing task. The architecture of UniRNNG is inspired by Principle and Parameter theory proposed by Noam Chomsky. UniRNNG utilises the linguistic typology knowledge available as feature-values within WALS database, to generalize over multiple languages. Once trained on sufficiently diverse polyglot corpus UniRNNG can be applied to any natural language thus making it Language-agnostic constituency parser. Experiments reveal that our proposed UniRNNG outperform state-of-the-art baseline approaches for most of the target languages, for which these are tested.