An automatic starting device for the engine, which quietly and quickly restarts the engine when a re-acceleration request is made by a driver, is provided. In a case where it is judged that a vehicle is decelerating and fuel injection is currently stopped, when it is then judged that a brake pedal is released and an engine rpm is smaller than an engine rpm which allows recovery from a fuel-supply stop state, the controller disengages a lock-up clutch. Upon detection of reverse rotation of the engine based on a detection signal of the crank-angle sensor, the controller controls a pinion gear to be pushed out by a lever of a starter to be meshed with a ring gear. After the ring gear is rotated by a predetermined angle, the controller rotary-drives a motor of the starter to restart the engine.