In this paper, a fuzzy multi-objective linear programming model is developed for solving a bi-criteria single machine scheduling problem. The objectives are to minimize the maximum lateness and total completion time. The membership function of each objective is defined as a piecewise linear function based on the acceptable satisfaction degrees determined by the decision maker. To solve the proposed model, the є- constraint method is then utilized which generats efficient solutions. Computational results show that the proposed approach is effective and can obtain better solutions in comparison with other conventional methods.