In order to improve the performance of Differential Evolution (DE) algorithm and extend its adaptability for solving continuous optimization problems, an enhanced DE algorithm was proposed by using efficient local search under the Memetic framework. Specifically, based on the Davidon-Fletcher-Powell (DFP) method, an improved local search method named NDFP was put forward, which could speed up finding locally optimal solutions based on excellent individuals explored by the DE algorithm. Furthermore, a strategy on when and how to run the NDFP local search was also given, so as to strike a good balance between global search (i.e., DE) and local search (i.e., NDFP). The proposed strategy was also enhanced the adaptability of NDFP local search in the range of DE algorithm. To verify the efficiency of the proposed algorithm, extensive simulation experiments were conducted on up to 53 test functions from CEC2005 and CEC2013 Benchmarks. The experimental results show that, compared with DE/current-to-best/1, SaDE and EPSDE algorithms, the proposed algorithm can achieve better performance in terms of both precision and stability.