Up to now, many numerical algorithms for strongly correlated electron systems have been proposed and applied to various systems, such as quantum Monte Carlo and Density Matrix Renormalization Group methods. However, the nature of the ground state of strongly correlated systems still remains a challenge because of the immaturity of numerical tools. In this thesis, we review Path Integral Renormalization Group (PIRG) method. This method can treat any type of lattice structure and it presents the possibility of efficient simulations which cannot be performed by other existing algorithms. We apply PIRG to the Hubbard model on square lattice. We expand on the numerical and technical details of PIRG and provide a benchmark result for 4 sites problem. Keywords: Path Integral Renormalization Group, Hubbard model, Slater determinants, strongly correlated electron systems