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). Reconstructing evolutionary tree is a major research problem in biology, and this problem is often known as phylogeny problem. The difficulty of such problem is that the number of possible evolutionary trees is very large. As the number of species increases, exhaustive enumeration of all possible relationships is not feasible. The quantitative nature of species relationships therefore requires the development of more rigorous methods for tree construction. The phylogeny problem is computationally intensive, thus it is suitable for distributed computing environment. Grid Computing (or Computational Grid) is a new concept to integrate the CPU power, the storage and other resources via Internet in order to get overall computing power. Nowadays, many bioinformaticists are developing the BioGrid technology in order to solve the challenges that need intensive computing in biology. In this paper, we design and develop a Grid-based system, and propose an efficient method based on the concept of quartet for solving the phylogeny problem on this architecture.