Because of its essential role in clean energy transition and low carbon economy, lithium is identified as a critical or strategic mineral by many countries or regions, including the US, EU, and China. Due to the unbalanced distribution of resources and production capacity and the separation of the primary lithium consuming and supplying countries, international trade is the main supply channel for lithium consuming countries to acquire enough resources. Comprehending the ability of the lithium trade network against external shocks is essential to supply security. To explore this issue, this paper employs complex network theory to construct a global lithium trading network system (LTNS) and simulates the robustness of LTNS under random and malicious attacks against cascading failures with a nonlinear load-capacity model. Results show that (1) Overall, the robustness of LTNS is poor under random and malicious attacks. (2) Rationally decreasing nodes' total import volume can enhance the robustness of LTNS. (3) A network with a tight link represents poor robustness against cascading failures. Meanwhile, the “head effect” in the network (the minority of nodes with the majority of resources) will make the networks more vulnerable. (4) Australia, Chile, and China have systemic impacts on LTNS. These findings may contribute to managing the supply of strategic raw materials more effectively for the policymakers.