To assess risk spillovers, this paper proposes a new GARCH copula quantile regression-based CoVaR model in which the nonlinear tail dependence is allowed to change with risk levels. Based on MSCI index daily data, we investigate the risk spillovers from four financial markets to the financial system of developed market. We find that Germany displays the largest risk spillovers, followed by France, the US and the UK, and that the risk spillovers are much larger during the COVID-19 pandemic than during the periods of the financial crisis and sovereign debt crisis.