Nelder-Mead method is a powerful mathematical technique for multidimensional unconstrained optimization. The other merit of the Nelder-Mead method is that it does not require any derivative information, which makes it suitable for exploitation in non-smooth regions. This paper proposes a new memetic algorithm incorporating Nelder-Mead method for local search. Nelder-Mead method coupling with GA will lead to utilization of more information derived from mathematical principle in the search process, thereby increasing the efficiency of search. The effectiveness of the proposed algorithm has been demonstrated in a case study of optimization of a fuzzy control system.