In molecular dynamics, molecular mechanics and quantum mechanics for a complicated system, most of the numerical calculations are at the Lennard-Jones potential. So, effective treatment of Lennard-Jones potential shows an important role. This paper presents an effective algorithm for the optimization of Lennard-Jones potential. The algorithm is a genetic-based algorithm associated with the owerful discrete gradient method and the correct choice of initial coordinates. Numerical results show the effectiveness of the present algorithm and new bestresults for 39,40,42,48,55,75,76,97 atoms were found. These results might be used to study the structure of spherical viruses and molecules.