The present invention provides a light emitting device driver circuit and a control circuit and a control method thereof. The light emitting device driver circuit includes a power stage circuit, a feedback circuit, and a control circuit. The control circuit includes a comparison circuit, a hysteresis control circuit, and a bleeder circuit. The control circuit generates an analog control signal according to a rectified dimmer signal and an output signal, for controlling the power stage circuit to regulate an output current, which is supplied to a light emitting device circuit to determine its brightness. When the analog control signal decreases to a predetermined hysteresis low level, the light emitting device driver circuit operates in a cut-off mode wherein the bleeder circuit consumes a bleeder current so as to maintain the output current at a zero current, for keeping the light emitting device circuit OFF.