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.