This paper proposes a new hierarchical packet scheduling algorithm, HDDRR, enhanced from the existing dynamic deficit round-robin (DDRR) to provide relative differentiated service that enables support of delay-sensitive applications over the Internet. The level of service differentiation can be adjusted with parameter. The HDDRR scheduler utilizes the property of DDRR, therefore it can achieve high throughput efficiently and simultaneously provide small delay for short packets of each class. This feature is of great importance for improving the playback quality of delay-sensitive applications. Simulation results showing the effectiveness of HDDRR are also presented.