This paper proposes a method for suppressing the speed vibration caused by the angular transmission error in cycloid gears used in industrial robots. It is important for industrial robots to have high accuracy. However, cycloid gears with an angular transmission error may cause vibration in the arms of a robot. The proposed method for compensating for the speed vibration uses a new extended state observer that is based on a model that considers a cycloid gear with an angular transmission error. A compensation current is generated by using the torque vibration which is converted from the estimated speed vibration. The speed vibration is suppressed using this compensation current. The experimental results show that the proposed system suppresses the vibration at the load speed.