This paper deals with the total weighted tardiness and earliness penalties for lot-streaming flow shop scheduling problems. A discrete differential evolution (DDE) algorithm with job permutations based representation is proposed. In the proposed DDE algorithm, the DE-based evolution is used to perform global exploitation, and a local search procedure based on the insert and swap neighborhood structure is used to enhance the exploration capability, and a restart scheme is employed to avoid the stagnation of the evolution. Extensive computational simulations and comparisons are provided, which demonstrate the effectiveness of the proposed DDE algorithm.