Considering flow shop scheduling problem with more objectives, will help to make it more practical. For this purpose, we have intended both the makespan and total due date cost simultaneously. Total due date cost is included the sum of earliness and tardiness cost. In order to solve this problem, a genetic algorithm is developed. In this GA algorithm, to further explore in solution space a Tabu Search algorithm is used. Also in selecting the new population, is used the concept of elitism to increase the chance of choosing the best sequence. To evaluate the performance of this algorithm and performing the experiments, it is coded in VBA. Experiments results and comparison with GA is indicated the high potential of this algorithm in solving the multi-objective problems.