There are many uncertain factors in job shop scheduling problems. However, those uncertainties are critical for the scheduling procedures. The imprecise processing times are modeled as triangular fuzzy numbers (TFNs) and the due dates are modeled as trapezium fuzzy numbers in this paper. A multi-objective genetic algorithm is proposed to solve fuzzy job shop scheduling problems, in which the objective functions are conflicting. Agreement index (AI) is used to show the satisfaction of client which is defined as value of the area of processing time membership function intersection divided by the area of the due date membership function. The multi-objective function is composed of maximize both the minimum agreement and maximize the average agreement index. Two benchmark problems were used to show the effectiveness of the proposed approach. Experimental results demonstrate that the multiobjective genetic algorithm does not get stuck at a local optimum easily, and it can solve job-shop scheduling problems with fuzzy processing time and fuzzy due date effectively.