An LED driver uses a positive-to-floating boost converter topology to generate a negative voltage −Vee relative to ground. The converter receives an input voltage. Vin from a power supply. One end of an output inductor is coupled to ground, and the other end of the inductor is coupled between a highside switch and a low side switch. The bottom terminal of the lowside switch generates −Vee. The anode end of an LED string is coupled to Vin and the cathode end is coupled to −Vee. The converter detects the LED current and regulates the switching duty cycle so that the LED current is equal to a target current. This is more efficient than coupling the anode end of an LED string to ground and the cathode end to −Vee. A conventional buck controller IC may be used.