This paper presents a nonlinear multi-objective mathematical model to obtain quality solutions for design problems of cellular manufacturing systems. The objectives of the multi-objective model are, simultaneously, (1) to minimize the number of exceptional elements among manufacturing cells, (2) to minimize the number of voids in a cell, and (3) to minimize cell load variation. In this paper, a new multi-objective genetic algorithm (GA) approach has been proposed to solve the multi-objective problem. In contrast to existing GA approaches, this GA approach contains some revised genetic operators and uses a conic scalarization method to convert the mathematical model's objectives in a single objective function. This approach has been tested and compared with two test problems and some source models collected from the literature. The results have shown that the problem-solving performance of the proposed multi-objective approach is at least as good as the existing approaches in designing the cellular system, and in many cases better than them.