Abstract: It is of great significance to study the flow shop scheduling problem with no-idle constrains, since no-idle production scheduling exists widely in modern industry. This paper proposes a multi-objective discrete sine optimization algorithm (MDSOA) to solve the mixed no-idle permutation flow shop scheduling problem (MNPFSP), whose goal is to minimize the makespan and the maximum tardiness. Firstly, an external archive set (AS) is established to store Pareto front and update after each iteration. Secondly, based on the basic sine optimization algorithm, the destruction reconstruction mechanism of the iterative greedy (IG) algorithm is introduced to redefine a location update strategy, whose key feature is suitable for discrete scheduling problems. Besides, both the fast non-dominate sorting method and the crowding distance are utilized to screen the population for retaining the elite solutions and ensuring the diversity and distribution of solutions. Finally, simulation experiments are made via 11 instances with different scales in Taillard Benchmark, which, together with the comparisons with NSGA-II and NSGA-III, demonstrate the effectiveness of the proposed MDSOA algorithm for solving MNPFSP.