In opportunistic networks, the use of social metrics (e.g., degree, closeness and betweenness centrality) of human mobility network, has recently been shown to be an effective solution to improve the performance of opportunistic forwarding algorithms. Most of the current social-based forwarding schemes exploit some globally defined node centrality, resulting in a bias towards the most popular nodes. However, these nodes may not be appropriate relay candidates for some target nodes, because they may have low importance relative to these subsets of target nodes. In this paper, to improve the opportunistic forwarding efficiency, we exploit the relative importance (called partial centrality) of a node with respect to a group of nodes. We design a new opportunistic forwarding scheme, opportunistic forwarding with partial centrality (OFPC), and theoretically quantify the influence of the partial centrality on the data forwarding performance using graph spectrum. By applying our scheme on three real opportunistic networking scenarios, our extensive evaluations show that our scheme achieves significantly better mean delivery delay and cost compared to the state-of-the-art works, while achieving delivery ratios sufficiently close to those by Epidemic under different TTL requirements.