Electrocardiogram (ECG) is the most widely used diagnostic tool to monitor the condition of the human heart. By using deep neural networks (DNNs), interpretation of ECG signals can be fully automated for the identification of potential abnormalities in a patient's heart in a fraction of a second. Studies have shown that given a sufficiently large amount of training data, DNN accuracy for ECG classification could reach human-expert cardiologist level. However, despite of the excellent performance in classification accuracy, DNNs are highly vulnerable to adversarial noises that are subtle changes in the input of a DNN and may lead to a wrong class-label prediction. It is challenging and essential to improve robustness of DNNs against adversarial noises, which are a threat to life-critical applications. In this work, we proposed a regularization method to improve DNN robustness from the perspective of noise-to-signal ratio (NSR) for the application of ECG signal classification. We evaluated our method on PhysioNet MIT-BIH dataset and CPSC2018 ECG dataset, and the results show that our method can substantially enhance DNN robustness against adversarial noises generated from adversarial attacks, with a minimal change in accuracy on clean data.