A driver for driving an LED backlight source is disclosed. The driver includes a boost converter for boosting inputted DC voltage and outputting boosted DC voltage to an LED series circuit having LEDs connected and a resistor in series, a feedback circuit for feeding back voltage across the resistor to a backlight driving circuit, and a control switch controlled by output of the backlight driving circuit depending on feedback voltage of the voltage across the resistor for keeping current flowing through the LED series circuit in a constant current. The driver drives the LED series circuit with a constant current, thereby prolonging lifetime of each LED of the LED series circuit. Furthermore, since a time period which the current flowing through the LED series circuit approaches to constant value is shorter, the driver has advantages over lower power consumption, faster response time and better operating efficiency.