– The purpose of this paper is to solve an assignment problem with linguistic costs/ times. In this paper, an assignment problem has been considered whose costs/times relating to the problem are linguistic variables and its solution methodology has been proposed. The solution method is based on fuzzy representation of linguistic costs/times and defuzzification of fuzzy costs/times. Here, a new defuzzification method based on statistical beta distribution has been used. Then the assignment problem has been converted into an assignment problem whose costs/times are crisp valued and solved by existing linear programming and/or Hungarian method. Finally, a numerical example has been considered and solved to illustrate the solution procedure