A control circuit of a LED driver utilizes a counter to acquire a cycle and a conduction time or a non-conduction time of an AC phase-cut voltage outputted by a TRIAC dimmer. A bleeding signal is determined according to the cycle and the conduction time or the non-conduction time and used for adjusting a bleeding current so as to avoid a flickering of the LED. The control circuit does not need extra pins for coupling a large capacitor, but the bleeding signal can be still acquired. Preferably, the present invention is suitable for an IC of low pin numbers.