We propose an efficient resource allocation scheme for big links in virtualized software-defined networking. Network virtualization based on software-defined networking provides big link concept to facilitate simple network management - big link maps a set of switches and links into a single virtual link. However, this paper reports an issue of the big link in that there is a severe performance degradation in virtualized SDN environments. We find the cause: the existing network hypervisors do not consider the network traffic when allocating physical resources to a big link. To address this issue, we present big link allocation scheme (BAS) that considers network traffic when allocating and reallocating resources to a big link. A prototype implementation is done with OpenVirteX, and experiments demonstrate that the big link with BAS achieves four times greater throughput than that of the big link without BAS. Moreover, by including a timer in OpenVirteX, the BAS decreases unnecessary resource reallocations, which reduces overhead.