Mobile virtual network operators (MVNOs) are mobile operators without their own infrastructure or government issued spectrum licenses. They purchase spectrum resources from primary mobile network operators (MNOs) to provide communication services under their own brands. MVNOs are expected to play an important role in mobile network markets, as this will increase the competition in retail markets and help to meet the demand of niche markets. However, with the rapidly increasing demand of mobile data traffic, efficient utilization of the limited spectrum resources owned by MVNOs has become an important issue. We propose here a resource sharing mechanism between MVNOs against the background of network functions virtualization (NFV). The proposed mechanism enables MVNOs to improve their quality of service (QoS) by sharing spectrum resources with each other. A nash bargaining solution based decision strategy is also devised to ensure the fairness of resource sharing. Extensive numerical evaluation results validate the effectiveness of the proposed models and mechanisms.