The invention discloses a driving circuit of an LED lamp and the LED lamp. A rectification filtration module performs rectification filtration treatment on an input alternating current mains supply, and first direct-current power is output; an LED driving module outputs driving voltage to LED lamp beads according to the first direct-current power, and thus the LED lamp beads are driven; a mains supply state monitoring module performs voltage monitoring through output of the rectification filtration module so as to detect the state of a switch panel of the LED lamp; a WIFI relay module generates a first control strategy according to the state of the switch panel, a first control signal is output to the LED driving module according to the first control strategy, thus the LED driving module is controlled to stop driving work when the rectification filtration module outputs first direct-current power, and the LED lamp beads are controlled to be turned off; and a WIFI relay power supply module keeps the WIFI relay module working normally when the LED lamp beads are turned off, the effect that the LED lamp beads are controlled to be turned off on the premise of no influence on the WIFI bridge connection function through simple and convenient on-off control can be achieved, operation is simple and convenient, and the using experience of a user for the LED lamp is greatly improved.