To deal with the disadvantages of Group Search Optimizer (GSO) as slow convergence, easy entrapment in local optima and failure to use history information, a Self-adaptive Group Search Optimizer with Elitist strategy (SEGSO) is proposed in this paper. To maintain the group diversity, SEGSO employs a self-adaptive role assignment strategy, which determines whether a member is a scrounger or a ranger based on ConK consecutive iterations of the producer. On the other hand, scroungers are updated with elitist strategy based on simulated annealing by using history information to improve convergence and guarantee SEGSO to remain global search. Experimental results demonstrate that SEGSO outperform particle swarm optimizer and original GSO in convergence rate and escaping from local optima.