A flux-controlled variable transformer can control voltage at a high speed without using any voltage adjusting tap. The transformer has a first and second magnetic circuits. The first magnetic circuit is composed of a first and second U-cut cores (13 and 11) which contact at their cut ends with each other in the state either of the two cores has been turned by 90.degree. in a twisting direction relative to the other. The primary winding (14) is wound in common around the second magnetic circuit and the first U-cut core (13) of the first magnetic circuit, the secondary winding (17) is wound around the second magnetic circuit and a control winding (12) is wound on the second U-cut core (11) of the first magnetic circuit. The magnetic flux linking the primary and secondary windings (14 and 17) can be controlled by change of the magnetic resistance in the first magnetic circuit with the primary winding (14) by changing a value of exciting current flowing in the control winding (12). Thus, the voltage in the secondary winding can be continuously changed by adjusting the exciting current flowing in the control winding.