As a key component of flow batteries, the flow field is to distribute electrolytes and to apply/collect electric current to/from cells. The critical issue of the flow field design is how to minimize the mass transport polarization at a minimum pressure drop. In this work a three-dimensional numerical model is proposed and applied to the study of flow field designs for a vanadium redox flow battery (VRFB). The performance of three VRFBs with no flow field and with serpentine and parallel flow fields is numerically tested. Results show that when a flow field is included a reduction in overpotentials depends not only on whether a flow field can ensure a more even distribution of electrolytes over the electrode surface, but also on whether the flow field can facilitate the transport of electrolytes from the flow field towards the membrane, improving the distribution uniformity in the through-plane direction. It is also shown that the pumping power varies with the selection of flow fields at a given flow rate. To assess the suitability of flow fields, a power-based efficiency, which takes account of both the cell performance and pumping power, is defined and calculated for different flow fields at different electrolyte flow rates. Results indicate that there is an optimal flow rate for each type of flow field at which the maximum efficiency can be achieved. As the cell with the serpentine flow field at the optimal flow rate shows the highest energy-based efficiency and round-trip efficiency (RTE), this type of flow field appears to be more suitable for VRFBs than the parallel flow field does.