A speed control system of a fan motor of an air conditioner is disclosed. A speed control system of a fan motor of an air conditioner comprises: an inverter having a power output terminal connected to a single-phase power input terminal of the fan motor which has a single-phase stator including a main coil and a sub coil, an induction rotor and a permanent magnet rotor installed between the stator and the induction rotor; and a three-phase driving motor connected to the power output terminal of the inverter and driving a compressor of an air conditioner by power received from the inverter.