An internal combustion engine starting device includes: a starting requirement determination device that determines whether an internal combustion engine is required to be started when the engine stops combustion by stopping fuel supply to the engine, and the vehicle is in a freewheel running; and a driving control device that drives and rotates a motor in a starter by increasing a driving voltage to the motor from a voltage changing device for changing the driving voltage supplied to the starter in a case where a travelling speed is high to be higher than in a case where the traveling speed is low, when the internal combustion engine is required to be started.