This thesis formally presents the resident physician scheduling problem, which is one of the most important scheduling problems in hospital. The resident physician scheduling problem is characterized as satisfying the fair schedule constraint, the physician specification constraint and the safe schedule constraint simultaneously. To minimize the penalties from violating the constraints, this study adopts the evolutionary approach to propose a genetic algorithm for solving the problems. In addition the well-known genetic operators, this study proposed a new mutation operator called dynamic mutation for solving the resident physician scheduling problem. The experimental results show that the proposed algorithm performs well in searching optimal schedules.