The permutation flowshop scheduling problem(PFSP) is a kind of classical production scheduling problem, which is ???? -hard. The traditional optimization method cannot be adopted to solve large scale problems. Therefore, this paper proposes a Memetic algorithm for the PFSP, in which a new neighbourhood structure based on NEH is developed. In addition, the size of the neighbourhood is dynamically adjusted during the search process. The computational results on Benchmark problems show that the proposed Memetic algorithm is effective and superior to a particle swarm optimization in the literature.