The steelmaking-continuous casting (SCC) is a bottleneck process in the steel production. Due to elevated product variety and environmental restrictions on the steelmaking industry, efficient operation of the SCC has become more crucial. This paper considers an SCC scheduling problem to minimize the weighted sum of total waiting time, total earliness, and total tardiness while satisfying the maximum waiting time and the continuous casting constraints. We propose a generic mixed integer linear programming (MILP) model that can express various SCC scheduling requirements. Using the MILP model, we develop an iterated greedy matheuristic inspired by the iterated greedy method. An initial SCC schedule is constructed by solving small MILP models one after another. Then, it is improved by solving a series of small MILP models representing the destruction and construction of the prior schedule. Through a numerical experiment, we show that the proposed algorithm can obtain efficient solutions in a short time and outperforms an NSGA-II algorithm for most test cases of practical size.