In today’s competitive business world, manufacturers need to accommodate customer demands with appropriate scheduling. This requires efficient manufacturing chain scheduling. One of the most important problems that has always been considered in the manufacturing and job-shop industries is offering various products according to the needs of customers in different periods of time, within the shortest possible time and with rock-bottom cost. Job-Shop Scheduling systems are one of the applications of group technology in industry, the purpose of which is to take advantage of the physical or operational similarities of products in various aspects of construction and design. In addition, these systems are identified as Cellular Manufacturing Systems (CMS). Today, applying CMS and the use of its benefits have been very important as a possible way to increase the speed of the organization’s response to rapid market changes. In this paper, a meta-heuristic method based on combining genetic and greedy algorithms has been used in order to optimize and evaluate the performance criteria of flexible job-shop scheduling problem. In order to improve the efficiency of the genetic algorithm, the initial population is generated in a greedy algorithm and several elitist operators are used to improve the solutions. The greedy algorithm which is used to improve the generation of the initial population prioritizes the cells and the job in each cell, and thus offers quality solutions. The proposed algorithm is tested over P-FJSP dataset and compared with the state-of-the-art techniques of this literature. To evaluate the performance of the diversity, spacing, quality and run-time criteria were used in a multi-objective function. The results of simulation indicate better performance of the proposed method compared to NRGA and NSGA-II methods.