With the emergence of cloud services based on data centers, demands for bandwidth-intensive applications have increased dramatically, and application services have transferred to a more diversified direction. Management as well as capacity of the backbone network needs further development to catch up with rapidly evolved application demands. Optical network virtualization can facilitate the sharing of physical infrastructure among multiple network applications. Virtual Network Embedding (VNE), the main implementation of network virtualization, determines how to map a virtual network request onto physical substrate. To expand the network capacity, flexible-grid elastic optical networks have been considered as a promising supporting technology for the future infrastructure of the next-generation Internet. However, due to the expense of key enabling equipment for flexible grid optical networks, the brown-field migration from a fixed grid to a flexible grid gave birth to the co-existing fixed/flexible grid. Based on the co-existing fixed/flexible grid optical networks, we investigate the problem of Virtual Optical Network (VON) provisioning, and present a flexible-grid-aware virtual network embedding algorithm to map the virtual networks onto the substrate network. In addition, the performance of the algorithm was evaluated under four different network scenarios. Simulation results show that the proposed algorithm can achieve better performance in all four scenarios.