This paper considers single machine scheduling problem. The objective is to determine sum of earliness and tardiness cost has been minimized. The memetic algorithm is developed to solve this problem. To evaluate performance of memetic algorithm, the solution of propose method is compare with the optimal solution. The results show that the average percentage deviation is less than 10. Here, the computational time required by the MA is significantly less than the time required by the optimal solution method. This result is more emphasized as the problem size is getting larger.