The blocking flow-shop scheduling problem (BFSP) with sequence-dependent setup times (SDST), which has important ramifications in the modern industry, is investigated in this paper. The SDST/BFSP is extended from the BFSP, which included the setup times in processing times. However, the setup times in actual processing depend on the preceding and successive jobs in the processing order. Hence, the setup times are considered independently of processing times in this paper. The mixed-integer linear programming (MILP) model of SDST/BFSP is designed. Furthermore, a discrete whale optimization algorithm (DWOA) based on problem-specific knowledge is proposed to solve certain SDST/BFSP. Firstly, a construction heuristic that depends on the properties of the problem is designed to reduce the blocking time and idle times created by SDSTs. Secondly, the leading whales in DWOA are replaced by the critical factories in SDST/BFSP. Further, three different search strategies including the searching for prey, encircling prey, and bubble-net attacking prey are designed to improve the exploitation and exploration capability of the DWOA. The statistical and computational experimentation in an extensive benchmark testified that the DWOA outperforms the state-of-the-art algorithms regarding efficiency and significance in solving SDST/BFSP.