A deterministic model for the transmission dynamics of HIV and Trichomonas vaginalis (TV) in a human population is designed and rigorously analysed. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease‐free equilibrium coexists with a stable endemic equilibrium whenever the associated reproduction number is less than unity. This phenomenon can be removed by assuming that the coinfection of individuals with HIV and TV is negligible. Furthermore, in the absence of coinfection, the disease‐free equilibrium of the model is shown to be globally asymptotically stable whenever the associated reproduction number is less than unity. Numerical simulation of the model, using initial and demographic data, shows that increased incidence of TV in a population increases HIV incidence in the population. It is further shown that control strategies, such as the treatment, condom use, and counselling of individuals with TV symptoms, can lead to the effective control or elimination of the HIV in the population if their effectiveness level is high enough. The time to disease elimination is reduced if more than one strategy (hybrid strategy) is considered.