The external controllability of the magnetic properties in topological insulators would be important both for fundamental and practical interests. Here we predict the electric-field control of ferromagnetism in a thin film of insulating magnetic topological insulators. The decrease of band inversion by the application of electric fields results in a reduction of magnetic susceptibility, and hence in the modification of magnetism. Remarkably, the electric field could even induce the magnetic quantum phase transition from ferromagnetism to paramagnetism. We further propose a transistor device in which the dissipationless charge transport of chiral edge states is controlled by an electric field. In particular, the field-controlled ferromagnetism in magnetic topological insulator can be used for voltage based writing of magnetic random access memories in magnetic tunnel junctions. The simultaneous electrical control of magnetic order and chiral edge transport in such devices may lead to electronic and spintronic applications for topological insulators. Introduction The recent discovery of the quantum anomalous Hall (QAH) effect has attracted intense interest in condensed matter physics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The QAH insulator is a new state of quantum matter which has a topologically nontrivial electronic structure characterized by a bulk energy gap but gapless chiral edge states, leading to the quantized Hall effect without an external magnetic field [16]. The edge channels of the QAH insulator conduct without dissipation, and thus has promising potential in the applications of low-power-consumption electronic devices. The QAH effect has been observed in thin films of Cr-doped [11-13] and V-doped [15] (Bi,Sb) 2 Te 3 magnetic topological insulators (MTIs), where robust bulk ferromagnetic (FM) ordering is spontaneously developed in this system even in the insulating regime.The ability to external control the magnetic properties of TIs [17][18][19] could be important both for fundamental and technological interest, particularly in view of recent developments in magnetoelectrics and spintronics [20,21]. In dilute FM semiconductors, the FM is mediated by itinerant charge carriers [22] and the magnetic ordering can be tuned by controlling the carrier density through an electric field [23]. But the electrical manipulation of magnetism in insulating MTIs has proved elusive. Recently, the magnetic ordering in TIs is shown to be related to the band topology [24], where the inverted band structure contributes a sizable Van Vleck magnetic susceptibility [6]. Here we propose the electric-field control of FM in an insulating MTI thin film. The band inversion is weakened by applying an electric field, leading to a reduction of the magnetic susceptibility, which is directly related to the magnetism. Remarkably, the electric field could even induce a quantum phase transition (QPT) from the FM phase to the paramagnetic (PM) phases. The thin film MTI with strong FM exhibits the QAH effect with chiral edg...