A voltage regulator includes a regulation MOS transistor and an amplifier providing an output for driving a gate of the regulation MOS transistor. The amplifier drives the gate based upon a difference between a reference voltage and a feedback voltage. The voltage regulator may further include a circuit for making the amplifier switch to a standby mode with low current consumption when the difference between the supply voltage and the output voltage of the regulator is below a first threshold. This is done while maintaining, at the gate of the regulation transistor, a voltage that keeps the regulation transistor on. The present invention is particularly applicable to the management of power supplies in portable telephones.