Planning software project is becoming more complicated and important as the size of software project grows. Many approaches have been proposed to help project managers by providing optimal staffing and scheduling in terms of minimizing the cost or time. Because previous approaches only concentrated on minimizing the cost or time, there has not been a study that considers software quality. We elucidated practical considerations regarding the software plan. Then, we defined a quality score by using those considerations in addition to task severity and defect amplification model. In this paper, we propose quality-based software project staffing and scheduling using a genetic algorithm (GA). Although we address quality, time is still critical. Thus, in the fitness function of the GA, time is also considered as a time bound. Our experiment indicates that our approach obtain the same duration as a time-based approach, but the quality score is higher than that of the time-based approach. By utilizing our approach, a project manager can obtain an appropriate plan by considering both quality and time.