In this paper, it is presented a heuristic method for solving the multi-objective flow shop problem. The work carried out considers the simultaneous optimization of the makespan and the flow time; both objectives are essential in measuring the production system's performance since they aim to reduce the completion time of jobs, increase the efficiency of resources, and reduce waiting time in queue. The proposed method is an adaptation of multi-objective Newton's method, which is applied to problems with functions of continuous variables. In this adaptation, the method seeks to improve a sequence of jobs through local searches recursively. The computational experiments show the potential of the proposed method to solve medium-sized and large instances compared with other existing literature methods.