An Optimum Communication Spanning Tree (OCST) problem is a problem of finding a spanning tree of minimum total communication cost satisfying a given set of requirements of communication. The popular technique for solving OCST problem is to use the heuristic algorithm. The heuristic approach does successfully obtain good solutions in a reasonable computational time. The particle swarm optimization-based (PSO) algorithm is one of the heuristic algorithms for optimization problems. In this work, we extend the concept of the particle swarm optimization-based (PSO) algorithm for the OCST problem proposed by Hoang et al. by combining the concept of adaptive inertia weight strategy to the velocity update step. We summarize the effect of the adaptive inertia weight over the proposed algorithm. In addition, we also introduce a new pattern of population initialization. Our proposed algorithm yields a better solution quality.