This study proposes a finite control-set model predictive current control (FCS-MPCC) scheme based on virtual voltage vectors for five-phase permanent magnet synchronous machines, which aims to reduce the low-order harmonic components of stator currents. In addition, comparing with traditional FCS-MPCC algorithms, the proposed algorithm retains fast control dynamic response and brings several other benefits: such as smaller burden of calculation, approximate constant switching frequency in entire speed operation range and lower current harmonics, especially for three-order harmonics. Furthermore, the one-step delay compensate solution of the proposed FCS-MPCC scheme in digital-controller implementation is presented. Finally, a series of computer simulation and hardware-in-loop (HIL) experimental tests are adopted to compare the performances of the proposed FCS-MPCC and two traditional FCS-MPCC schemes. Simulation and HIL experimental results have verified the validity and effectiveness of the proposed FCS-MPCC scheme using virtual voltage vectors.