The stability and sustainability of economic growth have always been a hot topic of concern in the academic and practical circles around the world. The purpose of this study is to examine the stability and sustainability of China's economic growth. For over 200 economies around the world, ensuring the stability and sustainability of their economic development in the face of sudden and catastrophic events is a great challenge. The COVID-19 epidemic in 2020 is just an emergency to test the economic development of each economy. The method adopted in this study is to observe the economic growth of more than 200 countries and regions in the world in 2020, visually measure the economic growth of each economy after being impacted by the COVID-19 epidemic, and then further explain the reason for the robustness of China's economic growth with the help of shock theory, statistical methods, including variance coefficient, nonlinear econometric model, shock entropy and other quantitative indicators. This study found that although the impact of the COVID-19 epidemic on China's economic growth is huge on the whole, the resilience of China's economic growth is significant, and the original trend of economic growth has not changed because of the impact of the COVID-19 epidemic. Its average variance coefficient is only 0.42, and the shock entropy is almost 0. The conclusion is that China's economic development is not only robust, but also sustainable. The practical significance of this study is that the perfect industrial economic structure and the Chinese style COVID-19 epidemic prevention and control model can still maintain the existing track of economic development at a certain cost of economic development, ensuring that the overall trend of economic growth remains strong, which lays a solid foundation for economic and social development after the COVID-19 epidemic.