Nowadays it is quite easy for common users to share and exchange resources on the Internet through application software based on peer-to-peer computing mode such as Gnutella, and therefore more and more people join in peer-to-peer network to share and exchange resources. As a result, the number of peers becomes extremely large, and resources are extremely abundant and scattered. In this case, it is a challenging job to do exhaustive search to retrieve all related resources for any query. In order to solve this problem, the authors present an incremental P2P search algorithm based on social acquaintance relationship (IPSBSAR). IPSBSAR mimics behaviors of peers in social networks to establish different semantic links among peers according to the level of knowing each other, and introduces a novel access and update mode of neighbor list to do incremental search. While IPSBSAR can do incremental search, it can also avoid copyright problems. Experiment results show that IPSBSAR can achieve high incremental query hit rate with low cost and low latency, and efficiently retrieve most of relevant resources when doing exhaustive incremental search with the same query semantic.