In this paper, a finite-control-set model predictive virtual-flux control (FCS-MPVFC) for a three-phase Vienna rectifier is developed and implemented to achieve voltage sensorless control, which is very robust to distorted grid-side voltage operation. Firstly, by investigating the relationship between virtual-fluxes aroused from grid-side voltages and line voltages in d-q frame, the control object is directly associated with virtual-flux tracking error minimization. Secondly, the reference line virtual-flux is calculated based on the controllability of active/reactive power associated with the delay compensation and load angle. Thirdly, to enhance the steady-state performance, switching sequence rather than single switching vector is utilized during one sampling period. Furthermore, a redundant vector pre-selection is adopted to balance the neutral-point voltage. The proposed strategy is compared with the traditional finite-control-set model predictive current control (FCS-MPCC) method. Both simulated and experimental results verify the effectiveness of the proposed control algorithm. INDEX TERMS Finite-control-set model predictive virtual-flux control, Vienna rectifier, voltage sensorless control, distorted, switching sequence, pre-selection. II. SYSTEM DESCRIPTION OF THREE-PHASE VIENNA RECTIFIER