A starting method for a variable speed accelerator including an electric device that generates a rotational drive force, and a transmission device that shifts the rotational drive force generated by the electric device to transmit the changed speed to an object to be driven, wherein the transmission device has a sun gear that rotates about an axis, a sun gear shaft that is fixed to the sun gear and extends in an axial direction about the axis, a planetary gear that meshes with the sun gear, revolves around the axis, and rotates about its own center axis, an internal gear that has a plurality of teeth aligned annularly about the axis and meshes with the planetary gear, a planetary gear carrier that has a planetary gear carrier shaft extending in the axial direction about the axis and supports the planetary gear so as to be revolvable around the axis and so as to be rotatable about the center axis of the planetary gear itself, and an internal gear carrier that has an internal gear carrier shaft extending in the axial direction about the axis and supports the internal gear so as to be rotatable about the axis, wherein the electric device has a constant speed electric motor that has a constant speed rotor that rotates the internal gear carrier shaft of the transmission device in a first direction, and a variable speed electric motor that has a variable speed rotor connected to the planetary gear carrier shaft of the transmission device, functions as a generator in a generator mode in which the variable speed rotor rotates in the first direction, and functions as an electric motor in an electric motor mode in which the variable speed rotor rotates in the second direction that is an opposite direction to the first direction, the starting method for the variable speed accelerator comprising: a variable speed electric motor start-up step in which the variable speed electric motor is started up at approximately a minimum rotational speed of the electric motor mode; a constant speed electric motor start-up step in which the constant speed electric motor is started up and the rotational speeds of the constant speed rotor and the internal gear in the first direction are gradually increased; a generator mode transition step in which the variable speed electric motor is made to set to the generator mode when a current value of the variable speed electric motor has reached a predetermined current value; and an electric motor mode transition step in which the variable speed electric motor is made to return to the electric motor mode in a case where the rotational speed of the constant speed electric motor has reached its rated rotational speed. a variable speed electric motor start-up step in which the variable speed electric motor is started up at approximately a minimum rotational speed of the electric motor mode; a constant speed electric motor start-up step in which the constant speed electric motor is started up and the rotational speeds of the constant speed rotor and the internal gear in the first direction are gradually increased; a generator mode transition step in which the variable speed electric motor is made to set to the generator mode when a current value of the variable speed electric motor has reached a predetermined current value; and an electric motor mode transition step in which the variable speed electric motor is made to return to the electric motor mode in a case where the rotational speed of the constant speed electric motor has reached its rated rotational speed.