Most replication-based packet forwarding algorithms in opportunistic networks neglect the fairness issue on the success rate distribution among all participants. In this paper we discuss the fairness evaluation on success rate, and propose a new fair packet forwarding strategy which operates as a plugin for traditional utility-based routing protocols. We compare the performance of our strategy with several well-known routing schemes via both a synthetic contact model and real human mobility traces. We find that our strategy improves the balance of success rates among users while maintaining approximately the same system throughput. In addition, our scheme reduces the cost of traditional utility-based routing protocols.