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The Job-Shop Scheduling Problem (JSSP) is a well-known and one of the challenging combinatorial optimization problems and falls in the NP-complete problem class. This paper presents an algorithm based on integrating Genetic Algorithms and Simulated Annealing methods to solve the Job Shop Scheduling problem. The procedure is an approximation algorithm for the optimization problem i.e. obtaining the minimum makespan in a job shop. The proposed algorithm is based on Genetic algorithm and simulated annealing. SA is an iterative well known improvement to combinatorial optimization problems. The procedure considers the acceptance of cost-increasing solutions with a nonzero probability to overcome the local minima. The problem studied in this research paper moves around the allocation of different operation to the machine and sequencing of those operations under some specific sequence constraint.