A phylogeny is a tree graph representation of genealogical relationships between biological objects. It is of general interest to estimate the phylogeny of whole organisms (species trees) using bio-molecular sequences. When multiple sequences are available for each organism such as with whole genome data, individual phylogenies estimated by each molecule (gene trees) may not be concordant. The lack of concordance may be due to actual biological mechanisms such as horizontal transfer of the molecules. Here, we present a new phylogeny estimation method designed to estimate the species tree despite such horizontal transfer. It uses the idea that horizontal transfer distorts distance relationships between pairs of species but a median estimate of the distances is robust to such distortions. We demonstrate the utility of our method using a simulation study.