The Job Shop Scheduling Problem (JSSP) is a well known practical planning problem in themanufacturing sector. We have considered the JSSP with an objective of minimizing makespan. In thispaper, we develop a three-stage hybrid approach called JSFMA to solve the JSSP. In JSFMA,considering a method similar to Shuffled Frog Leaping algorithm we divide the population in several subpopulations and then solve the problem using a Memetic algorithm. The proposed approach have beencompared with other algorithms for the Job Shop Scheduling and evaluated with satisfactory results on aset of the JSSP instances derived from classical Job Shop Scheduling benchmarks. We have solved 20benchmark problems from Lawrence’s datasets and compared the results obtained with the results of thealgorithms established in the literature. The experimental results show that JSFMA could gain the bestknown makespan in 17 out of 20 problems.