Most of the work about flowshop problems assumes that the problem data are known exactly at the advance or the common approach to the treatment of the uncertainties in the problem is use of probabilistic models. However, the evaluation and optimization of probabilistic model is computationally expensive and the application of the probabilistic model is rational only when the descriptions of the uncertain parameters are available from the historical data. In this paper we deal with a permutation flowshop, problem with fuzzy processing times. First we explain how to compute start and finish time of each operation on related machines for a given sequence of jobs using fuzzy arithmetic. Next we used a fuzzy ranking method in order to select the best schedule with minimum fuzzy makespan. We proposed an ant colony optimization algorithm for generating and finding good (near optimal) schedules.