Deployment of Voice over Internet Protocol (VoIP) is rapidly growing worldwide due to the new services it provides and cost savings derived from using a converged IP network. However, voice quality is affected by bandwidth, delay, latency, jitter, packet loss e.t.c. Latency is the dominant factor that degrades quality of voice transfer. There is therefore strong need for a study on the effect of Latency with the view to improving Quality of Voice (QoV) in VoIP network. In this work, Poisson probability theorem, Markov Chain, Probability distribution theorems and Network performance metric were used to study the effect of latency on QoS in VoIP network. This is achieved by considering the effect of latency resulting from several components between two points in multiple networks. The NetQoS Latency Calculator, Net-Cracker Professional® for Modeling and Matlab/Simulink® for simulating network were tools used and the results obtained compare favourably well with theoretical facts