The five-phase voltage source inverters (VSIs) have drawn more and more attention in the recent years, and required the extension of control schemes already well known for three-phase voltage source inverters. Nevertheless, the low-order harmonic currents suppression is a special issue of control methods for five-phase VSIs with the common-mode voltage (CMV) still remaining to be reduced. Model predictive current control (MPCC) method has been developed as a widespread and effective control technique in power electronics, especially for multiple constraints system, and has been applied to five-phase VSIs with the consideration of low-order harmonic currents suppression and CMV reduction, simultaneously. However, the complex cost function and huge computation amount in the existing works become another deficiency, and the weighting factors of different components in the cost function is difficult to adjust. In this paper, a new MPCC method based on virtual voltage vectors has been proposed for five-phase VSIs. The zero and medium voltage vectors have been eliminated and by this way the CMV can be reduced by 80%. Then, following the volt-second balance law, ten active virtual voltage vectors and active zero vectors are synthesized to acquire zero volt-second value in x-y subspace, as a consequence, low-order harmonic currents are suppressed. Finally, a simplified cost function without weighting factor is adopted. Simulation and experimental results have verified that the proposed MPCC method can reduce CMV by 80% and suppress low-order harmonic currents successfully.