Mathematical model for the effect of reverse transcriptase inhibitor on the dynamics of HIV-1 infection model with three delays is proposed and analyzed. We begin this model with proving the positivity and boundedness of the solution. We analyze the stability of the viral free steady state and the infected steady state of the system. Also we have carried out bifurcation analysis along with an estimated length of delay to preserve the stability behaviour. By developing a few Lyapunov functionals, we obtain conditions ensuring global stability of steady states. Numerical simulations are carried out to explain the mathematical conclusions. © 2014, Korean Society for Computational and Applied Mathematics.