VoIP has emerged as a very promising technology for future telecommunication networks. One of the most challenging aspects of successful deployment of VoIP systems is the inherent nature of IP that is not designed for real-time information transfer. This adversely affects the quality of transferred voice. To improve the quality of voice received through IP networks, a range of solutions have been proposed. Among the more recent solutions, one can name resource managers and admission control algorithms. In this paper a new algorithm for managing resources, specifically bandwidth, in VoIP systems is proposed to improve the quality of service and increase bandwidth utilization. The new RM algorithm was evaluated by running simulations for two different test topologies. Results show an improvement of 4%-8% in bandwidth utilization of the bottleneck link.