In this study, a genetic algorithm (GA) with priority-based representation is proposed for a flexible job shop scheduling problem (FJSP) which is one of the hardest operations research problems. Investigating the effect of the proposed representation schema on FJSP is the main contribution to the literature. The priority of each operation is represented by a gene on the chromosome which is used by a constructive algorithm performed for decoding. All active schedules, which constitute a subset of feasible schedules including the optimal, can be generated by the constructive algorithm. To obtain improved solutions, iterated local search (ILS) is applied to the chromosomes at the end of each reproduction process. The most widely used FJSP data sets generated in the literature are used for benchmarking and evaluating the performance of the proposed GA methodology. The computational results show that the proposed GA performed at the same level or better with respect to the makespan for some data sets when compared to the results from the literature.