The COVID-19 outbreak has greatly impacted the stability of the global financial markets. In the post-COVID-19 pandemic era, the risk contagion patterns of the global financial markets may change. This paper utilizes the conditional value-at-risk (ΔCoVaR) model to measure the risk level of the financial markets in various economies and uses the TVP-VAR-CONNECTEDNESS approach to construct a time-varying spillover index. Based on the dimensions of time and space, we explored the contagion path, contagion status, and contagion structure characteristics of global financial market risk before and during the COVID-19 pandemic. The results entail several conclusions. (i) The COVID-19 pandemic increased the spillover level of global financial market risk and the risk connectedness of financial markets in different countries. In addition, during the concentrated outbreak period of COVID-19, the risk spillover level in developing countries rose rapidly, while the financial risk spillover level in developed countries decreased significantly. (ii) The impact of the COVID-19 pandemic on the spillover of the global financial market risk is time-varying, and there is a strong correlation between the risk spillover level of the financial markets of the world and the severity of the COVID-19 pandemic. (iii) Due to the impact of the COVID-19 pandemic, Brazil, Canada, and Russia have become new risk spillover centers; in the post-COVID-19 pandemic era, China's spillover to developed countries has increased, and the financial influence of China has also gradually increased. In addition, the risk contagion capacity of financial markets among European countries is gradually converging. (iv) During the concentrated outbreak of the COVID-19 pandemic, the Americas were the main exporter of global financial market risk, while Europe played a role in risk absorption.