Scheduling real time and non real time packets at network nodes has an important impact by reducing theprocessing overhead, queuing delay and response time. Most of the existing packet scheduling algorithmsused in network based on First-In First-Out (FIFO), non-preemptive priority, and preemptive priorityscheduling. However, these algorithms incur a large processing overhead, queuing delay and responsetime and are not dynamic to the data traffic changes. In this paper, we present a new hierarchicalscheduling algorithm to assign priority, Hierarchical Hybrid EDF/FIFO which can not only serve the realtime traffic but also provide best effort service to non real time traffic. To examine our approach forscheduling, we realized our analytical study to express the worst case queuing delay and the worst caseresponse time for different traffics. The simulation results showed that the Hierarchical hybrid EDF/FIFOachieved the minimum packet delay and adequate loss packet for non real time traffic when compared withHierarchical FIFO. In general, the performances of our approach draw near to Hierarchical EDF whichconfirms the effectiveness of this approac