An isolated flyback converter for an LED driver includes a snubber circuit unit connected to the primary side of a transformer; and a snubber voltage detection unit which detects a snubber voltage of the snubber circuit unit and generates a reference voltage proportional to the detected snubber voltage. Further, the isolated flyback converter includes a switching unit with a source terminal and a drain terminal, and may be turned on or off in response to an arbitrary logic signal. Furthermore, the isolated flyback converter includes a control unit which compares a voltage supplied through the switching current sensing resistor with the reference voltage, and supplies a logic signal at relatively high level or relatively low level to the switching unit to control the switching unit such that a secondary-side current of the transformer is maintained relatively constant.