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• In this paper, a delayed HIV-TB co-infection model has been formulated. • The existence and stability of equilibrium points have been shown. • The condition under which Hopf-bifurcation takes place has been determined. • Ideal timing of the combination of treatment for both diseases has been computed. In this paper, a non-linear mathematical model for HIV-TB co-infection has been proposed. A constant time delay parameter is introduced into the model which accounts for the delay in detection and the commencement of appropriate treatment for co-infected individuals. The basic reproduction number along with the location and existence of equilibrium points is computed. Local stability analysis of all the equilibrium points in the presence of delay parameter is performed, which gives certain conditions, under which Hopf-bifurcation takes place. Numerical simulations are performed with different set of parameters for each equilibrium point to explore the effect of delay in detection and treatment of the infected individuals. The numerical results have also been used to describe the rich dynamics generated by the system in the presence of delay. [ABSTRACT FROM AUTHOR]