A novel differential evolution (DE) algorithm, namely DE_TWET, is presented to deal with the no-wait flow-shop scheduling problem (NFSSP) with sequence-dependent setup times (SDSTs) and release dates (RDs). The criterion is to minimize a total weighted earliness/tardiness (TWET) cost function. The presented algorithm is a hybrid of DE, problem’s properties, and a special designed local search. In DE_TWET, DE is adopted to execute global search in the solution space, and the problem’s properties are utilized to give a speed-up evaluation method and construct the local search, and the special local search is designed to enhance the local search ability of DE. Experimental results and comparisons demonstrate the effectiveness and robustness of the presented algorithm.