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Abstract Cascading failures are emergent phenomena on interdependent networks and plenty of models have been proposed to explore the features of cascading failures. However, few of them focus on energy-supported dependence relations between interdependent networks including control nodes. In this paper, a load-based energy-supported cascading failure model is proposed on interdependent networks, where the energy control factor λ and control nodes are considered. According to the numerical simulations, it is found that as the energy control factor λ increases, both interdependent Erdős–Rényi (ER) networks and scale-free (SF) networks become more vulnerable. Meanwhile, with the increase of energy control factor λ , interdependent SF networks become more robust than ER networks against random failures. In addition, increasing the power exponent γ can improve the robustness of interdependent SF networks. Finally, although coupling preferences and control node setting strategies have few impacts on cascading failures on interdependent ER networks, the assortative coupling preference (AC) and betweenness control node setting strategy (BS) can improve the robustness of interdependent SF networks. Highlights • An energy-supported cascading failure model is proposed on interdependent networks. • Increasing factor λ makes interdependent SF networks more robust than ER networks. • Increasing exponent γ improves the robustness of interdependent SF networks. • The AC and BS can improve the robustness of interdependent SF networks. [ABSTRACT FROM AUTHOR]