Recent studies have highlighted adversarial examples as ubiquitous threats to the deep neural network (DNN) based speech recognition systems. In this work, we present a U-Net based attention model, U-Net$_{At}$, to enhance adversarial speech signals. Specifically, we evaluate the model performance by interpretable speech recognition metrics and discuss the model performance by the augmented adversarial training. Our experiments show that our proposed U-Net$_{At}$ improves the perceptual evaluation of speech quality (PESQ) from 1.13 to 2.78, speech transmission index (STI) from 0.65 to 0.75, short-term objective intelligibility (STOI) from 0.83 to 0.96 on the task of speech enhancement with adversarial speech examples. We conduct experiments on the automatic speech recognition (ASR) task with adversarial audio attacks. We find that (i) temporal features learned by the attention network are capable of enhancing the robustness of DNN based ASR models; (ii) the generalization power of DNN based ASR model could be enhanced by applying adversarial training with an additive adversarial data augmentation. The ASR metric on word-error-rates (WERs) shows that there is an absolute 2.22 $\%$ decrease under gradient-based perturbation, and an absolute 2.03 $\%$ decrease, under evolutionary-optimized perturbation, which suggests that our enhancement models with adversarial training can further secure a resilient ASR system.