Voice over IP(VoIP) and Voice over ATM(VoA) are two research hotspots in the fields of communication technology. One of the main problems degrading the QoS in VoIP and VoA is the longer time delay when speech packets are transmitted from a speaker to a listener. This paper discusses in detail the composition of time delay and the influence of different parts of delay on speech quality under IP and ATM network environments. The author puts forward a new method to convert usual CBR code streams into VBR streams for the purpose of reducing time delay from one terminal to another, which can avoid the dilemma between compressing the bit rates of speech sources and reducing assembly delay of speech packets.