Primary human immunodeficiency virus (HIV) infection is characterized by an initial exponential increase of viral load in peripheral blood reaching a peak, followed by a rapid decline to the viral setpoint. Although the target-cell-limited model can account for part of the viral kinetics observed early in infection [Phillips, 1996. Reduction of HIV concentration during acute infection: independence from a specific immune response. Science 271 (5248), 497-499], it frequently predicts highly oscillatory kinetics after peak viremia, which is not typically observed in clinical data. Furthermore, the target-cell-limited model is unable to predict long-term viral kinetics, unless a delayed immune effect is assumed [Stafford et al., 2000. Modeling plasma virus concentration during primary HIV infection. J. Theor. Biol. 203 (3), 285-301]. We show here that extending the target-cell-limited model, by implementing a saturation term for HIV-infected cell loss dependent upon infected cell levels, is able to reproduce the diverse observed viral kinetic patterns without the assumption of a delayed immune response. Our results suggest that the immune response may have significant effect on the control of the virus during primary infection and may support experimental observations that an anti-HIV immune response is already functional during peak viremia.