Due to the fact that there is a lack of comprehensive understanding of how the dynamic nature of supply chain networks (SCNs) interrelates with network structures, particularly network topologies under disruptions. This research employs a novel evolving model of a supply chain network (SCNE model) by modifying the Barabási and Albert (BA) model to capture the phenomenon of regional economy and the factor of firms’ attractiveness, considering the degree, the locality preference, and the heterogeneity of SCN members simultaneously. We then analyze the SCNE model via the mean-field theory and conduct simulation study to identify the scale-free characteristic of the proposed supply chain network model. Additionally, we leverage node and edge removal to emulate random and targeted disruptions. We measure and compare the robustness of four network models, i.e., the SCNE model, the Erdos and Rényi (ER) model, the BA model, and the Watts and Strogatz (WS) model using two essential metrics, i.e., the size of the largest connected component and the network efficiency. We find that the robustness of the SCNE model is better than the BA model and the WS model on the whole in the presence of disruptions. Also, from the node level, the SCNE model maintains resilience, behaving similarly to the ER model against random disruptions while it shows vulnerability under targeted disruptions, responding in line with the BA model and the WS model. From the edge level, the network efficiency of the SCNE model changes slowly, and the topological structure of the SCNE model slightly changes initially but decreases rapidly at some value, as well as the BA model, the WS model, and the ER model. Based on the results, we summarize key points of the implications for research and practice in supply chain management.