In this article, we investigate systemic risk of 157 insurers around the globe. We construct tail risk networks among these insurers using a single-index model for quantile regressions with a variable selection technique. We develop a new network-based systemic risk indices, taking into account expected tail losses of insurers, direct and indirect contagion effects, and the time-varying strength of tail risk spillover. Our systemic risk indices successfully recognize global systemically important insurers (G-SIIs). We find that on average G-SIIs are more systemically relevant than non-G-SIIs, particularly during the recent U.S. financial crisis. We also find a small group of non-G-SIIs that are more important than G-SIIs. Our results have significant implications for systemic risk regulation.