Conventional single-phase Vienna rectifiers employ proportional-integral (PI) controllers which are appropriate for controlling DC components, to regulate their line currents. However, in the regions close to the line current’s zero-crossing point, the dynamics of PI controllers are too slow to respond to the reference current, which has an AC component. Hence, the power factor (PF) of the device is degenerated, and total harmonic distortion (THD) increases. A controller with a fast dynamic response is thus required to solve this problem. In this paper, we investigate the use of a model-based predictive controller (MPC), which has a faster dynamic response than a PI controller, to improve the line current quality of a single-phase Vienna rectifier. With this method, the average current in both the continuous current mode (CCM) and the discontinuous current mode (DCM) of operation are controlled using a mode detection method. Moreover, we calculate the optimized duty cycle for the single-phase Vienna rectifier, by predicting the next current state. We verify the operation of the proposed algorithm using a PSIM simulation, and a practical experiment conducted with a 1-kW-rated single-phase Vienna rectifier prototype. With the proposed method, the quality of the line current near the zero-crossing point is improved, and the PF is controlled to unity.