A fuzzy goal programming model for the simple U-line balancing (SULB) problem with multiple objectives is presented. In real life applications of the SULB problem with multiple objectives, it is difficult for the decision-maker(s) to determine the goal value of each objective precisely as the goal values are imprecise, vague, or uncertain. Therefore a fuzzy goal programming model is developed for this purpose. The proposed model is the first fuzzy multi-objective decision-making approach to the SULB problem with multiple objectives which aims at simultaneously optimizing several conflicting goals. The proposed model is illustrated using an example. A computational study is conducted by solving a large number of test problems to investigate the relationship between the fuzzy goals and to compare them with the goal programming model proposed by Gken and Apak (Gken, H. and Apak, K., European Journal of Operational Research, 171, 577-585, 2006). The results of the computational study show that the proposed model is more realistic than the existing models for the SULB problem with multiple objectives and also provides increased flexibility for the decision-maker(s) to determine different alternatives.