An LED driver comprising a power converter for powering an LED unit and a control unit for controlling the power converter is provided. The power converter comprising an input terminal for receiving a rectified AC supply voltage, and an output terminal for supplying a current to the LED unit, and the control unit comprising —an input for receiving a supply signal representative of the supply voltage and —an output for providing a control signal to the power converter The control unit is further arranged to: —determine the control signal for controlling the power converter based on the supply signal, and —control the power converter to supply the current to the LED unit based on the control signal, the current being amplitude modulated in synchronism or in phase with the rectified AC supply voltage.