Ever since the discovery of a molecular clock, many methods have been, developed to reconstruct the molecular evolutionary phylogenetic trees. We deal with this problem from the viewpoint of an inductive inference and apply J. Rissanen's (1986) minimum description length principle to extract the minimum complexity phylogenetic tree. Our method describes the complexity of molecular phylogenetic tree by three terms which are related to the tree topology, the sum of branch lengths and the difference between the model and the data measured by logarithmic likelihood. Five mitochondrial DNA sequences from human, common chimpanzee, pygmy chimpanzee, gorilla and orangutan are used for investigating the validity of this method. It is suggested that this method is superior to the traditional method in that it still shows good accuracy even near the root of phylogenetic trees.