A low drop-out voltage regulator having soft-start. A low drop-out regulator circuit is provided having an input node, an output node, a power FET connected by a source and drain between the input node and the output node, and a feedback circuit having an output connected and providing a control signal to a gate of the power FET. A current limit circuit is configured to control the power FET to limit the current through it when the voltage across a controllable sense resistor connected to conduct a current representing the current through the power FET exceeds a predetermined limit value. At start-up, control unit provides a control signal to the controllable resistor to cause the resistance value of the controllable resistor to decrease incrementally in value at respective predetermined incremental times during a predetermined time interval.