An extensive mathematical model for HIV-HCV co-infection is developed. The positivity and boundedness of the model under investigation is established using well-known theorems. The next generation matrix method is used to construct the basic reproduction number for the model. The local and global stabilities of the model are shown using the linearization and Lyapunov function approaches, respectively. Bifurcation analysis and sensitivity analysis of the model are also presented. The findings from the simulations will be presented accordingly.