Provided is an engine starting device, including: starter control means for causing, when the restart condition is established during a period in which a meshing inhibition condition for a ring gear and a pinion gear is established, the pinion gear and the ring gear to mesh with each other after the meshing inhibition condition is released, thereby restarting the engine. The starter control means determines the meshing permission condition and the meshing inhibition condition based on at least an engine rotation speed, and determines the release of the meshing inhibition condition before the engine completely stops based on at least one of the engine rotation speed and an elapsed time after the establishment of the meshing inhibition condition.