Abstract: We propose a new conditional risk measure, conditional generalized value-at-risk (CoGVaR), from the perspective of measuring systemic risk. The new class of risk measures is a natural generalization of the conditional quantiles including the classic CoVaR. Compared with the classic conditional value-at-risk (CoVaR) and conditional expectile (CoExpectile), it has more potential application in reality as it takes the risk attitude of the decision maker into consideration, which has not been the focus of much study to date. Using generalized quantile regression approach with state variables added, some calculation results are presented in the Dow Jones U.S. Financials Index case, and it is shown that it provides a new perspective on systemic risk contribution. In addition, the result shows that our risk measure can capture the tail risk by using more convex disutility function.