An apparatus for driving LEDs. The apparatus that drives a first LED unit having at least one LED and second LED unit connected to the first LED unit and having at least one LED comprises a rectifying unit for rectifying an AC power source connected to the first LED unit, a first current detector connected between the rectifying unit and the first LED unit and having its operation state changed depending on a level of current flowing through the first LED unit, a second current detector connected between the rectifying unit and the second LED unit and having its operation state changed depending on a level of current flowing through the second LED unit, and a reverse current protector connected between the first and second current detectors for providing a path to connect the first and second LED units in series.