The Lennard-Jones (LJ) Potential Energy Problem is to construct the most stable form of N atoms of a molecule with the minimal LJ potential energy. This problem has a simple mathematical form Minimize subject to Where ,is the coordinates ofatom. This paper is to minimize the L-J potential on ,where n = 3N. however it is a challenging and diffcult problem for many optimization methods when N is larger. This paper presents an effective mathematical optimization algorithm for minimizing the LJ Potential and a series of elegant optimal solutions of atoms up to 310 were got.