This paper proposes a memetic computing algorithm by incorporating Eager Random Search (ERS) into differential evolution (DE) to enhance its search ability. ERS is a local search method that is eager to move to a position that is identified as better than the current one without considering other opportunities. Forsaking optimality of moves in ERS is advantageous to increase the randomness and diversity of search for avoiding premature convergence. Three concrete local search strategies within ERS are introduced and discussed, leading to variants of the proposed memetic DE algorithm. The results of evaluations on a set of benchmark problems have demonstrated that the integration of DE with Eager Random Search can improve the performance of pure DE algorithms while not incurring extra computing expenses.