The invention discloses a bridgeless electrolytic-capacitor-free low-ripple-wave high-power constant-current power supply of an LED lamp. The bridgeless electrolytic-capacitor-free low-ripple-wave high-power constant-current power supply of the LED lamp comprises an alternating-current power supply circuit, a control circuit, a coupling-out circuit and a ripple wave restraining circuit. The alternating-current power supply circuit comprises a constant-current drive chip U1, a constant-current drive chip U2, an alternating-current positive half-wave current loop and an alternating-current negative half-wave current loop, wherein the constant-current drive chip U1 and the constant-current drive chip U2 are controlled by the positive half-wave and the negative half-wave of an alternating-current power supply Uin. The current of the alternating-current positive half-wave current loop and the current of the alternating-current negative half-wave current loop both flow through a primary winding N11 and a primary winding N12 of a magnetic integration transformer TR so that an induced voltage can be generated on a secondary winding NV1 and a secondary winding NV2, and then the working voltage of the constant-current drive chip U1 and the working voltage of the constant-current drive chip U2 are provided through the control circuit. An induced secondary current is generated on a center post secondary winding N2 and is output to the loaded LED lamp through the coupling-out circuit. The ripple wave restraining circuit restrains current ripple waves. According to the bridgeless electrolytic-capacitor-free low-ripple-wave high-power constant-current power supply of the LED lamp, a bridge rectifier and an electrolytic capacitor are not adopted, so that the electric power is increased, the reliability is improved, the drive capability of the chips is improved through expanded current, the working temperature of the chips is lowered, the service life of the chips is prolonged, the constant-current precision is high, the current ripple waves are small, the LED lamp does not flicker, and the circuits meet the environmental-friendliness principle.