As a result of the evolvement in instant messaging (IM) software and the technique for voice over data networks, recently the voice over IP (VoIP) is becoming popular. The VoIP applications produce a lot of voice packets flowing into the Internet. These voice packets no doubt introduce a heavy burden for the network. Moreover, for the voice packets to be delivered in the IP network, additional packet headers, such as IP, UDP and RTP, are needed. These overhead bits will significantly reduce the bandwidth efficiency. In this paper, we introduce a mechanism for multiplexing a number of voice packets from different streams into a larger packet. By this way, the additional headers can be reduced. We use the Multiprotocol Label Switching Protocol (MPLS) to establish a label switched path (LSP) between the two IP-GWs at both ends. Along the LSP, the bandwidths required for voice packets are reserved. In order to improve the bandwidth efficiency, we suggest using speech activity detection (SAD) technique for voice sources by which the voice packets are suppressed when a source is in silence periods.