In the modern data networks, the demand is increasing for interruption free, high speed, and best quality of services to perform successful communications. This paper emphasizes on the high priority (HP) traffic like video conferencing, video streaming, telemedicine, teleconferencing, and interactive gaming for the real time communications. To achieve the best quality data communication for the HP traffic, in this paper, we propose a new dynamic bandwidth allocation (DBA) algorithm called dynamic hybrid slot-size bandwidth allocation (DHSSBA) algorithm, which is the modified version of existing hybrid slot-size/rate (HSSR) algorithm. The performance of the proposed scheme has been analyzed by using numerical simulations in terms of the end-to-end packet delay, absolute delay variation, jitter, and throughput for both the HP and best effort (BE) traffic. We have also compared the simulation results of the proposed scheme with those of the existing modified HSSR (MHSSR), delay variation guaranteed protocol (DVGP), and HSSR schemes. From the comparison of the simulation results, at the highest offered load of 1.0, it can be seen that for the HP traffic the proposed scheme provides 60%, 50%, and 20% less average end-to-end delay than the existing HSSR, DVGP, and MHSSR schemes, respectively. At the highest offered load of 1.0, the proposed scheme also provides about 35% higher throughput than both the HSSR and DVGP schemes with 45% and 35% less jitter variation than the HSSR and DVGP schemes, respectively.