Monitoring the evolution of hydrogen gas on carbon steel pipe using acoustic emission (AE) signal can be a part of a reliable technique in the modern structural health-monitoring (SHM) field. However, the extracted AE signal is always mixed up with random extraneous noise depending on the nature of the service structure and experimental environment. The noisy AE signals often mislead the obtaining of the desired features from the signals for SHM and degrade the performance of the monitoring system. Therefore, there is a need for the signal denoising method to improve the quality of the extracted AE signals without degrading the original properties of the signals before using them for any knowledge discovery. This article proposes a non-decimated stationary wavelet transform (ND-SWT) method based on the variable soft threshold function for denoising hydrogen evolution AE signals. The proposed method filters various types of noises from the acquired AE signal and removes them efficiently without degrading the original properties. The hydrogen evolution experiments on carbon steel pipelines are carried out for AE data acquisition. Simulations on experimentally acquired AE signals and randomly generated synthetic signals with different levels of noise are performed by the ND-SWT method for noise removal. Results show that our proposed method can effectively eliminate Gaussian white noise as well as noise from the vibration and frictional activity and provide efficient noise removal solutions for SHM applications with minimum reconstruction error, to extract meaningful AE signals from the large-scale noisy AE signals during monitoring and inspection.