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From the beginning of the 21st century,fourth party logistics(4PL)has been attracting more and more attention in the field of academic and industry.In this paper,a 4PL routing problem(4PLPR)with fuzzy duration time is presented,and the fuzzy numbers is used to denote the uncertainty of duration time.After a simple description of it,an integer programming for the problem is built.Then a hybrid Self Organizing Migrating Algorithm is designed.A high adaptive length-variant coding method formed by two arrays stand together is used to represent the individual where the individual corresponds to a path as a solution.Generate such individuals to form the initial group by Kth shortest algorithm.After migrating,best individual in the current generation is selected according to the fitness function.Finally,an extensive computational analysis is presented and the numerical results show that which route should be selected in order to get minimum cost in the due date.