Controlling and designing quantum magnetic properties by an external electric field is a key challenge in modern magnetic physics. Here, from first principles, the effects of an external electric field on the magnetocrystalline anisotropy (MCA) in ferromagnetic transition-metal monolayers are demonstrated which show that the MCA in an Fe(001) monolayer [but not in Co(001) and Ni(001) monolayers] can be controlled by the electric field through a change in band structure, in which small components of the p orbitals near the Fermi level, which are coupled to the d states by the electric field, play a key role. This prediction obtained opens a way to control the MCA by the electric field and invites experiments.