Aimed at the no-idle flow-shop scheduling problem (NIFSP) with minimized makespan, a discrete sine optimization algorithm (DSOA) is proposed. Inspired by sine waveforms, the original sine optimization algorithm (SOA) is a global optimization algorithm, which uses the sine function to update the position of search agents. First, the update position strategy to adapt to the combinatorial optimization problem is redefined. An iterated greedy algorithm with a variable removing size is employed to update the position to enhance the exploration ability. Then, a crossover strategy and a selection strategy are applied to avoid the algorithm falling into local optimum. Next, to improve the exploitation ability of local search and the accuracy of the algorithm, an insertion-based local search scheme is applied in DSOA to search for a better solution around the current optimal solution. Finally, based on the Taillard benchmark, the simulation results of performance comparisons are presented. The experimental results demonstrate the effectiveness of the proposed DSOA algorithm for solving NIFSP.