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In today's modern era of Big data, computationally efficient and scalable methods are needed to support timely insights and informed decision making. One such method is sub-sampling, where a subset of the Big data is analysed and used as the basis for inference rather than considering the whole data set. A key question when applying sub-sampling approaches is how to select an informative subset based on the questions being asked of the data. A recent approach for this has been proposed based on determining sub-sampling probabilities for each data point, but a limitation of this approach is that appropriate sub-sampling probabilities rely on an assumed model for the Big data. In this article, to overcome this limitation, we propose a model robust approach where a set of models is considered, and the sub-sampling probabilities are evaluated based on the weighted average of probabilities that would be obtained if each model was considered singularly. Theoretical support for such an approach is provided. Our model robust sub-sampling approach is applied in a simulation study and in two real world applications where performance is compared to current sub-sampling practices. The results show that our model robust approach outperforms alternative approaches.