The COVID-19 pandemic has emphasized the awareness of avoiding contact with shared or public devices, such as those used in traditional biometric systems. Common biometric systems, including fingerprint, palmprint, and iris recognition, require physical contact with the device, which increases the risk of contracting infectious diseases. As a result, non-contact biometric systems, such as gait recognition, may be increasingly important in the future. In this paper, we present an accurate gait recognition system that uses pressure sensing mats. Our proposed system employs high-density pressure sensing mats that significantly reduce computational complexity when compared to traditional gait recognition methods that use cameras. We acquired pressure distribution data from 30 subjects, including 19 males and 11 females, and developed an algorithmic framework that involves data preprocessing and classification to identify different subjects. We implemented five supervised machine learning models as classifiers, and our results indicate that the Convolutional Neural Networks (CNN) model performed the best, with a classification accuracy of 92.08%. Our study shows that the proposed gait recognition system is an effective non-contact biometric system that can distinguish different individuals with high accuracy. The use of pressure sensing mats reduces the risks associated with physical contact, making it a promising solution for biometric recognition in public spaces during the ongoing COVID-19 pandemic. In conclusion, our research contributes to the development of non-contact biometric systems and presents a viable solution for future applications.