Virtualization improves the efficiency of networks by allowing multiple virtual networks to share a single physical network's resources. Next-generation optical transport networks are expected to support virtualization by accommodating multiple virtual networks with different topologies and bit rate requirements. Meanwhile, Optical Orthogonal Frequency-Division Multiplexing (OOFDM) is emerging as a viable technique for efficiently using the optical fiber's bandwidth in an elastic manner. OOFDM partitions the fiber's bandwidth into hundreds or even thousands of OFDM subcarriers that may be allocated to services. In this paper, we consider an OOFDM-based optical network and formulate a virtual network mapping problem for both static and dynamic traffic. This problem has several natural applications, such as e-Science, Grid, and cloud computing. The objective for static traffic is to maximize the subcarrier utilization, while minimizing the blocking ratio is the aim for dynamic traffic. Two heuristics are proposed and compared. Simulation results are presented to demonstrate the effectiveness of the proposed approaches.