We propose a new genetics-based approach to scheduling parallel program tasks on multiprocessors. In the presence of communication delays, it is shown that task duplication is a useful technique for shortening the length of schedules. Though some genetic algorithms (GAs) for multiprocessor scheduling have been proposed so far, none of them allows task duplication. To overcome this deficiency, we develop a new GA, incorporating new genetic operators to control the degree of replication of tasks. Through simulation studies, we show that the proposed GA works effectively, especially when communication delays are relatively small.