Domain wall motion in materials exhibiting perpendicular magnetic anisotropy has been the subject of intensive research because of its large potential for future spintronic devices. Recently, it has been shown that perpendicular anisotropy of thin films can be influenced by electric fields. Voltage-controlled magnetic switching has already been realized, which is envisioned to lead to low-power logic and memory devices. Here we demonstrate a radically new application of this effect, namely control of domain wall motion by electric fields. We show that an applied voltage perpendicular to a Co or CoB wire can significantly increase or decrease domain wall velocities. Velocity modification over an order of magnitude is demonstrated (from 0.4 to 4 μm s(-1)), providing a first step towards electrical control of domain wall devices. This opens up possibilities of real-time and local control of domain wall motion by electric fields at extremely low power cost.