A phylogenetic tree is a graph whose vertices correspond to biological species and whose edges correspond to genetic changes between the species at the two end points. Typically the leaves represent extant species while interior nodes represent ancestral species. There are many methods in current use to construct phylogenetic trees given, for example, certain DNA sequences at the leaves. This paper proposes a novel heuristic method to determine phylogenetic trees given numerical distances between the extant species. \par The method generates a low-cost Steiner tree for appropriately located species in a higher-dimensional space. For $n$ extant species, the originally given distances yield an $n \times n$ symmetric dissimilarity matrix $\Delta$. Multidimensional scaling is then used to represent the species as points in a $d$-dimensional Euclidean space, with $d < n$, such that their Euclidean distances match the dissimilarity matrix $\Delta$ as closely as possible. A Steiner minimum tree (SMT) is a tree of minimum Euclidean length that interconnects the terminals, typically containing junctions that are not among the given terminals. An heuristic method is utilized to estimate an SMT for the given set of vertices, and this tree is proposed as the phylogenetic tree. \par Several approaches are utilized to validate this phylogenetic method. Results of computational experiments are reported, and comparisons are made with classic methods such as Neighbor Joining.