Measles virus is a member paramyxoviridae within the genus of morbillivirus. Its genome consist of approximately 16,000 bases of non-segmented single stranded negative sense RNA. This means that the virus is transcribed immediately upon entry into the cell. The virus spreads from person to person through the release of the aerosol droplets. In this paper, we investigate the transmission of measles virus using the five compartments of susceptible, vaccinated, exposed, infectious and recovered individuals with demographic factors. We give the mathematical model describing the transmission of the measles virus. The results of the model analysis showed that the model has a unique disease free equilibrium (DFE) which is locally asymptotically stable when 𝑅0 < 1 and unstable when 𝑅0 > 1. We further carried out numerical simulation of the model to investigate the effect of vaccination on the transmission dynamics of the virus. The results showed that there exist a minimum value of the vaccine efficacy below which herd immunity cannot be achieved. We further observed that increasing the vaccine efficacy above this critical value will lower the herd immunity of the population.