A group scheduling problem, which is production scheduling problem associated with the concept of group technology, is studied under due date constraints in multi-stage manufacturing systems. The purpose of this paper is to develop and evaluate a practical heuristic procedure for determining group sequence and job sequence within each group to minimize total tardiness in multi-stage manufacturing systems. A heuristic algorithm has been developed by introducing the concept of relative measures of job tardiness and group tardiness for job sequencing and group sequencing, respectively. A numerical example is shown to illustrate the proposed procedure. The heuristic algoirthm is tested by comparisons with problems with known optimal solutions and also with random group schedules for a set of large-size problems. Results indicate that the proposed heuristic algorithm provides good solutions with small computational requirements, and thus is viable for large size problems in practice.