Priority Queueing(PQ) guarantees that traffics with higher priorities get higher Quality of Service(QoS), whereas the performances of those with lower priorities are poor, therefore reducing the total performances and fairness. A scheduling algorithm is proposed combining Priority and bandwidth Requirement Queueing(PRQ), which adopts bandwidth requirement to modulate scheduling probabilities on the base of priority scheduling, aiming to increases the scheduling probabilities of traffics with lower priorities, to improve their QoS and the total performances, and to receive better fairness as well. The simulation results show that PRQ significantly improves the QoS of traffics with lower priorities and the total performances, beating PQ on fairness.