In view of the importance of flexible job-shop scheduling problem (FJSP) in actual production, this paper constructs a mathematical model of fuzzy FJSP and then proposes a mixed quantum algorithm based on local optimization strategy and improved optimization rotation angle. For improving the production process, a double chain coding method was designed with two gene chains, which respectively represent the machine selection and the process sequencing. Next, the hybrid quantum particle swarm optimization (QPSO) was introduced to ensure the scheduling efficiency. Finally, the prototype system of the proposed strategy was simulated by using some actual examples. The results show that the proposed algorithm can quickly form an adjusted plan that has minimal difference from the original plan. INDEX TERMS Flexible job-shop scheduling, quantum particle swarm optimization, quantum gate rotation angle, double chain quantum coding.