As a complex network, eco-industrial symbiosis network is featured with complexity, openness, and non-linearity. A methodology is proposed to analyze and optimize the eco-industrial symbiosis network from the perspective of complex network theory. Structural robustness index and performance robustness index are established as the analysis model. Consequently, a robust method is developed to optimize the eco-industrial symbiosis network system based on the percolation theory. A conceptual framework is put forward to improve the robustness of eco-industrial symbiosis network system by introducing the "spare core" enterprise which is validated by quantitative analysis. The empirical results show that the robustness of eco-industrial symbiosis network varies under both random failure and intentional disturbance scenarios. However, eco-industrial symbiosis network system has strong self-regulation capability as long as the core enterprise is still in operation. It is recommended that supplementary chain could be added to those enterprises with lower network node connectivity to form "spare core" enterprise. This can not only effectively reduce the dependence of other enterprises on core enterprises, but also further improve the robustness of eco-industrial symbiosis network. This methodology is practically validated by a case analysis of eco-industrial park in China. The findings provide useful inputs to the design and operation of eco-industrial parks.