Disclosed is a driving circuit for a Light Emitting Diode (LED) lamp, the LED lamp containing the driving circuit and a method for operating the driving circuit. The driving circuit includes: three alternating voltage input terminals, including two alternating voltage input terminals for receiving an alternating voltage and one common terminal, the two alternating voltage input terminals are controlled so that at least one alternating voltage input terminal receives the alternating voltage from a power supply; a constant current control circuit receiving the alternating voltage through at least one alternating voltage input terminal and outputting a constant direct current to an LED load, the constant current control circuit includes a constant current control chip having a maximum on-time pin; and a three-stage dimming detection control circuit including a variable control resistor for three-stage dimming control, and is controlled by the alternating voltage received by at least one alternating voltage input terminal so that the variable control resistor is connected to the maximum on-time pin with different resistance values, and the constant current control chip outputs three different current levels according to a resistance value of the connected variable control resistor.