An actual hybrid flow shop scheduling (HFSS) problem with operation skipping is investigated from the steelmaking continuous casting (SCC) process, which plays a vital role in the productive processing of a slab in iron and steel enterprises. Firstly, a mixed integer mathematical model is explored for this problem based on the previous survey. Secondly, a block heuristic method based on double-layer right shift is presented on the basis of the problem-specific characteristics, which can generate the better initial solution for the problem. Thirdly, an improved memetic algorithm (IMA) with double-vector-representation based on attribution feature is proposed for dealing with the problem, which includes the block heuristic for initialization, the novel mutation structure on the basis of the problem-specific characteristics, and the enhanced local research to improve the exploitation ability. Finally, to test the performance of the IMA, a large number of instances from a steel plant are adopted. By statistical analysis, the results of experiment evaluation indicate that the proposed IMA has highly effective performance and obvious advantages comparing with other well-known algorithms. Note to Practitioners—Due to the change of order and the technology requirements of SCC process, partial charges must be further refined to eliminate the impurities or heat molten steel. This study models a novel hybrid flow shop scheduling problem with operation skipping, in which all charges undergo the primary refining stage, and partial ones undergo the double or triple refining stage. The average sojourn time, the total earliness and the total tardiness are taken as the objective functions, and the constraint for operation skipping is added. We develop an IMA based on the attribution feature of charge, in which double-vector-representation is designed, and a novel mutation structure on the basis of the problem-specific characteristics is presented, and an enhanced local research is p...