Control device for an electric compressor and a start control method of an electric compressor that can smoothly and reliably start the electric compressor even at high temperature. Even in a high temperature state of a power transistor, a rotational speed or an acceleration rate of a motor according to the temperature is set to gradually start the electric compressor. After the commencement of the start, the temperature of the power transistor is repeatedly checked for every predetermined time to update the rotational speed or the acceleration rate of the motor, and the rotational speed or the acceleration rate of the motor is increased according to the temperature of the power transistor, thereby allowing quick start.