Infecting Aedes aegypti mosquitoes with the bacteria Wolbachia has been proposed as an innovative new strategy to reduce the transmission of dengue fever. Field trials are currently being undertaken in Queensland, Australia. However, few mathematical models have been developed to consider the persistence of Wolbachia-infected mosquitoes in the wild. This paper develops a mathematical model to determine the persistence of Wolbachia-infected mosquitoes by considering the competition between Wolbachia-infected and non-Wolbachia mosquitoes. The model has four steady states that are biologically feasible: all mosquitoes dying out, only non-Wolbachia mosquitoes surviving, and two steady states where non-Wolbachia and Wolbachia-infected mosquitoes coexist. The stability of the steady states is determined with respect to the key parameters in the mosquito life cycle. A global sensitivity analysis of the model is also conducted. The results show that the persistence of Wolbachia-infected mosquitoes is dominated by the reproductive rate, death rate, maturation rate and maternal transmission. For the parameter values where Wolbachia persists, it dominates the population, and hence the introduction of Wolbachia has great potential to reduce dengue transmission.