In this paper, aiming at incorporating reactive power compensation functionality into the Vienna rectifiers, a modified one-cycle-control (MOCC) strategy is proposed by which the three-phase Vienna rectifier can be regulated in leading, lagging or unity power factors with near-sinusoidal input current waveform. First, a brief review of the working principle of the conventional OCC (COCC) strategy is conducted. Then, the MOCC strategy with the functionality of input current phase-shift control is discussed in detail. To mitigate input current distortion caused by the current phase-shift, a method whereby the signal of one phase current which is flowing in an uncontrollable region is injected into the other two phases' current command signals is further presented. The constraints to the implementation of the MOCC scheme and the reactive power compensation capacity of the rectifier under MOCC control are analyzed as well. The proposed MOCC strategy is as easy to implement as the COCC strategy. Moreover, the MOCC strategy also preserves all other advantages of the COCC strategy, such as no phase-locked loop, no frame transformation and constant switching frequency. Finally, the theoretical analysis of the proposed MOCC strategy is fully verified by simulation and experimental results from a 1 kV·A three-phase Vienna rectifier prototype.