Generally the Flowshop Scheduling Problem (FSSP) is a production environment problem where a set of jobs has to visit a set of machines in the same order. In permutation flow shops the sequence of jobs is the same on all machines with the objective of minimizing the sum of completion timesusing Genetic Algorithm. A significant research effort has been devoted for sequencing jobs in a flowshop for minimizing the make span. No machine is allowed to remain idle when a job is ready for processing. This paper, describes the Permutation Flowshop Scheduling Problem (PFSSP)solved by using Genetic Algorithm (GA) to minimize the makespan. The basic concept of genetic algorithm is, that it is developed for finding near to optimalsolution for the minimum makespan of the jobs, machines permutation flowshop scheduling problem. It shows that the innovative genetic algorithm approach which provides competitive results for the solution of Permutation Flowshop Scheduling Problem.