Recurrent Neural Networks (RNNs) are among the most successful machine learning models for sequence modelling, but tend to suffer from an exponential increase in the number of parameters when dealing with large multidimensional data. To this end, we develop a multi-linear graph filter framework for approximating the modelling of hidden states in RNNs, which is embedded in a tensor network architecture to improve modelling power and reduce parameter complexity, resulting in a novel Recurrent Graph Tensor Network (RGTN). The proposed framework is validated through several multi-way sequence modelling tasks and benchmarked against traditional RNNs. By virtue of the domain aware information processing of graph filters and the expressive power of tensor networks, we show that the proposed RGTN is capable of not only out-performing standard RNNs, but also mitigating the Curse of Dimensionality associated with traditional RNNs, demonstrating superior properties in terms of performance and complexity.