In the field of spintronics, researchers have manipulated magnetization using spin-polarized currents. Another option is to use a voltage-induced symmetry change in a ferromagnetic material to cause changes in magnetization or in magnetic anisotropy. However, a significant improvement in efficiency is needed before this approach can be used in memory devices with ultralow power consumption. Here, we show that a relatively small electric field (less than 100 mV nm-1) can cause a large change (∼40%) in the magnetic anisotropy of a bcc Fe(001)/MgO(001) junction. The effect is tentatively attributed to the change in the relative occupation of 3d orbitals of Fe atoms adjacent to the MgO barrier. Simulations confirm that voltage-controlled magnetization switching in magnetic tunnel junctions is possible using the anisotropy change demonstrated here, which could be of use in the development of low-power logic devices and non-volatile memory cells.