Optimal management model in BitTorrent-like peer-to-peer (P2P) file sharing system can be reduced into a min–max programming problem subject to addition-min fuzzy relation inequality. To deal with such problem, we introduce the concept of optimal vector. Besides, a novel optimal-vector-based (OVB) algorithm is developed to find a minimal optimal solution. Based on practical application consideration, solution obtained by the OVB algorithm is theoretically demonstrated to be better than or equal to that obtained by the existing method. Advantage of our proposed OVB algorithm is illustrated by detailed numerical examples.