Worldwide, network virtualization has attracted attention as a promising network technology and is expected to be utilized in new-generation networks. In this paper, we propose a topology design and admission control approach for such network virtualization with improved network robustness of both the physical and virtual networks. In our proposed method, first we construct a new network graph that includes the performance of the nodes. We construct a new Laplacian matrix to evaluate the network robustness of the physical networks. Then, based on a user's request, a topology of a virtual network is determined with the KMB algorithm. This topology design is represented as a minimum Steiner tree problem. Moreover, by using admission control, the virtual network is created so as not to degrade the network robustness of the physical networks. If the network robustness of physical networks is degraded, the user's request is rejected and the virtual network is not created. With a simulation, we evaluated the performance of our proposed topology design and admission control approach. Numerical examples show that by using our proposed method, a large number of virtual networks can be provided for users. Moreover, the network robustness of the virtual networks can be improved. Our proposed method is effective for improving the network robustness of both the physical and virtual networks.