In this paper, we present swarm based Resource Minimization Scheme (RMS) for Network-Coding-based Multicast System (NCMS). The main objective of the RMS is to reduce network coding links while maintaining the desired rate of a multicast system. The resource minimization problem in NCMS is NP-Hard. In this paper, we apply the Binary Particle Swarm Optimization (BPSO) algorithm to the resource minimization problem in NCMS. The numerical results show the effectiveness of the proposed BPSO based RMS in comparison to the previously proposed algorithms.