The present invention relates to a driving circuit (100) connected to a conventional phase-cut dimmer. A LED light source (30) is driven by a switched mode power supply (26), which is powered by the mains voltage through a phase-cut dimmer (10) and a rectifier (22). The current through the LED light source (30) is reduced according to the voltage level of the average rectified voltage Vin detected by a voltage sensor (24) and the on time limitation of the switched mode power supply (26). The current amplitude will be increasingly reduced towards the low voltage levels of Vin, namely towards the low dimmer knob levels. Thereby, the invention allows a LED light source driving circuit (100) connected to a conventional phase-cut dimmer to readily make the dimming curve of the LED light source (30) non-linear for being more compatible with the human eye sensitivity.