A mathematical model with cytotoxic cells of hepatitis B virus (HBV) infection is set up based on a basic model of virus dynamics without cytotoxic cells and experimental observation of anti-viral drug therapy for HBV infection patients. A quantitative analysis of dynamic behaviors shows that the model has three kinds of equilibrium points, which represent the patient's complete recovery without immune ability, complete recovery with immune ability, and HBV persistent infection at the end of the treatment with drug lamivudine, respectively. Our model may provide possible quantitative interpretations for the treatments of chronic HBV infections with the drug lamivudine, in particularly explain why the plasma virus of Nowak et al.'s patients turnover the original level after stopping the lamivudine treatment.