Brain-inspired Hyper-dimensional computing (HDC) has recently shown promise as a lightweight machine learning approach. Despite its success, there are limited studies on the robustness of HDC models to adversarial attacks. In this paper, we introduce the first comparative study of the robustness between HDC and deep neural network (DNN) to malicious attacks. We develop a framework that enables HDC models to generate gradient-based adversarial examples using state-of-the-art techniques applied to DNNs. Our evaluation shows that HDC with a proper neural encoding module provides significantly higher robustness to adversarial attacks than existing DNNs. In addition, HDC models have high robustness to adversarial samples generated for DNNs.