We report results of first principles calculations for effects of an external electric field (E-field) on the magnetocrystalline anisotropy (MCA) in transition-metal (Fe, Co, and Ni) monolayers and at metal-insulator (Fe/MgO) interfaces by means of full-potential linearized augmented plane wave method. For the monolayers, the MCA in the Fe monolayer (but not in the Co and Ni) is modified by the E-field, and a giant modification is achieved in the $Fe_{0.75}Co_{0.25}$. For the Fe/MgO interfaces, the ideal Fe/MgO interface gives rise to a large out-of plane MCA, and a MCA modification is induced when an E-field is introduced. However, the existence of an interfacial FeO layer between the Fe layer and the MgO substrate may play a key role in demonstrating an Efield-driven MCA switching, i.e., from out-of-plane MCA to in-plane MCA.