It is often assumed that it is not possible to alter the properties of magnetic materials once they have been prepared and put into use. For example, although magnetic materials are used in information technology to store trillions of bits (in the form of magnetization directions established by applying external magnetic fields), the properties of the magnetic medium itself remain unchanged on magnetization reversal. The ability to externally control the properties of magnetic materials would be highly desirable from fundamental and technological viewpoints, particularly in view of recent developments in magnetoelectronics and spintronics. In semiconductors, the conductivity can be varied by applying an electric field, but the electrical manipulation of magnetism has proved elusive. Here we demonstrate electric-field control of ferromagnetism in a thin-film semiconducting alloy, using an insulating-gate field-effect transistor structure. By applying electric fields, we are able to vary isothermally and reversibly the transition temperature of hole-induced ferromagnetism.