In biological research, scientists often need to use the information of the species to infer the evolutionary relationship among them. The evolutionary relationships are generally represented by a labeled binary tree, called the evolutionary tree (or phylogenetic tree). The phylogeny problem is computationally intensive, and thus it is suitable for parallel computing environment. In this paper, a fast algorithm for constructing neighbor-joining phylogenetic trees has been developed. The CPU time is drastically reduced as compared with sequential algorithms.