For stability and reliability of real-world applications, the robustness of DNNs in unimodal tasks has been evaluated. However, few studies consider abnormal situations that a visual question answering (VQA) model might encounter at test time after deployment in the real-world. In this study, we evaluate the robustness of state-of-the-art VQA models to five different anomalies, including worst-case scenarios, the most frequent scenarios, and the current limitation of VQA mod- els. Different from the results in unimodal tasks, the maximum confidence of answers in VQA models cannot detect anomalous inputs, and post-training of the outputs, such as outlier exposure, is ineffective for VQA models. Thus, we propose an attention-based method, which uses confidence of reasoning between input images and questions and shows much more promising results than the previous methods in unimodal tasks. In addition, we show that a maximum entropy regularization of attention networks can significantly improve the attention-based anomaly detection of the VQA models. Thanks to the simplicity, attention-based anomaly detection and the regularization are model-agnostic methods, which can be used for various cross-modal attentions in the state-of-the-art VQA models. The results imply that cross- modal attention in VQA is important to improve not only VQA accuracy, but also the robustness to various anomalies.