A linear LED driver includes a voltage supply terminal providing a driving voltage, at least one first transistor, each of which has an input terminal coupled to a respective LED, and a bleeder circuit. When the voltage of the output terminal of each of the at least one first transistor is lower than a first threshold and a power voltage is higher than a second threshold, the bleeder circuit will generate a bleeder current to discharge the voltage supply terminal so as to prevent the LEDs from flickering. The bleeder circuit detects the voltage of the output terminal of each of the at least one first transistor. Therefore, whether the LEDs are lighted up can be confirmed so that the bleeder current can be provided at properly time point.