Solving non-linear equations is frequently encountered in practice; methods of solving the problem are generally iterative, such as Newton, gradient, conjugate direction, variable metric, Aitken procedure, etc. Group Search Optimizer (GSO) is a new population based swarm intelligent algorithm inspired by the animal searching behavior. However, the exploitation capability is not very well. In this paper, the limited storage Quasi-Newton method is incorporated into Group Search Optimizer (GSO) to increase the local search capability. To test the performance, the authors apply it to solve non-linear equations.