There are provided an LED driving apparatus and an LED driving method thereof. The LED driving apparatus includes: a light emitting unit including one or more LEDs, a rectifying unit rectifying an input signal to generate a first signal; a signal conversion unit inverting a waveform of a first signal to generate a second signal; and an operation unit arithmetically operating the first and second signals. A plurality of AC signals each having a different waveform are arithmetically operated to generate a signal having a small amount of a ripple component, and an LED is driven by the signal, thus preventing a lifespan of the LED from being shortened by omitting a smoothing electrolytic capacitor, one of main causes shortening the lifespan of an LED driving circuit.