An energy converting device having an eccentric rotor includes a fixed portion and an eccentric rotor. This fixed portion has a central axis, an outer frame, and several fixed coil portions. The eccentric rotor has a bearing, a rotatory shaft, an eccentric arm, an eccentric shaft portion, a supporting plate, an inner annular magnetic portion, and an outer annular magnetic portion. The inner magnetic portion and the outer magnetic portion are concentric and aligned with the eccentric shaft portion. The eccentric shaft portion is offset from the rotary shaft. When the rotary shaft of the eccentric rotor rotates, these fixed coil portions cut through the inner magnetic portion and the outer magnetic portion repeatedly, so magnetic flux passing through the coils alternates accordingly to generate electromotive force. Conversely, it can be used as an electric motor. In addition, it can be integrated with a cycloidal speed reducer to form a motor with speed reduction and torque augmentation capability. The integrated cycloidal motor is compact, does not need a shaft coupler to transmit power from a motor to the reducer, and therefore may operate more smoothly.