The use of antiretroviral therapy has proven to be remarkably effective in controlling the progression of human immunodeficiency virus (HIV) infection and prolonging patient's survival. Therapy however may fail and therefore these benefits can be compromised by the emergence of HIV strains that are resistant to the therapy. In view of these facts, the question of finding the reason for which drug-resistant strains emerge during therapy has become a worldwide problem of great interest. This paper presents a deterministic HIV-1 model to examine the mechanisms underlying the emergence of drug-resistance during therapy. The aim of this study is to determine whether, and how fast, antiretroviral therapy may determine the emergence of drug resistance by calculating the basic reproductive numbers. The existence, feasibility and local stability of the equilibriums are also analyzed. By performing numerical simulations we show that Hopf bifurcation may occur. The model suggests that the individuals with drug-resistant infection may play an important role in the epidemic of HIV.