Despite the high performance achieved by deep neural networks on various tasks, extensive research has demonstrated that small tweaks in the inputs can lead to failure in the model's predictions. This issue affecting deep neural networks has led to a number of methods to improve model robustness, including adversarial training and distributionally robust optimization. Although both of these two methods are geared towards learning robust models, they have essentially different motivations: adversarial training attempts to train deep neural networks against perturbations, while distributional robust optimization aims to improve model performance on the most difficult ``uncertain distributions". In this work, we propose an algorithm that combines adversarial training and group distribution robust optimization to improve robust representation learning. Experiments on three image benchmark datasets illustrate that the proposed method achieves superior results on robust metrics without sacrificing much of the standard measures.