In this paper, we propose a new hybrid genetic algorithm with a fuzzy logic controller. The proposed algorithm considers both the preemptive case and the non-preemptive one of activities among jobs. For dealing with the preemptive and non-preemptive cases in genetic algorithm (GA), we develop a new gene-representation method for GA, and also use fuzzy logic controller (FLC) for regulating GA parameters. For experimental comparison, we divide the proposed algorithm to two modes; the GA with the FLC (pro-fGA) and the GA without the FLC (pro-GA). These two sub-algorithms are applied to several job-shop scheduling problems in numerical examples, Various experiment results obtained show that the pro-fGA outperforms the pro-GA.