At present, the non-dominated sorting genetic algorithm-Ⅱ (NSGA-Ⅱ) is used widely in researches of flexible job-shop multi-objective rescheduling problem. Because of the excessive elite reservation, the algorithm is easily precocious, thus the performance of multi-objective optimization algorithm could be improved. By analyzing the research status and insufficiency of multi-objective flexible job-shop scheduling problem (FJSP), a multi-objective FJSP optimization model was put forward, in which the makespan, processing cost and processing quality were considered. According to the above model, a modified non-dominated sorting genetic algorithm (NSGA-Ⅱ) with close relative variation was designed. In this algorithm, the chromosome mutation rate was determined after calculating the blood relationship between the two cross chromosomes. Crossover and mutation strategies of NSGA-Ⅱ were optimized, and the prematurity of population was overcome. Finally, the performance of the proposed model and algorithm was evaluated through a case study, and the results demonstrated the efficiency and feasibility of the proposed model and algorithm.