A system for automatically stopping and starting an engine of a vehicle which enables proper determination of whether the stopping of the engine is possible, in accordance with the state of a battery. A power brought out from the battery by auxiliaries is subtracted from a power generated by a generator, thereby calculating a difference corresponding to a power for actually charging the battery. By sequentially adding the value, an integrated value of power charged in the battery is calculated. Meanwhile, a value of a known power WBRK consumed by a brake lamp plus a current power consumed by the auxiliaries is multiplied by a beforehand determined target value of idling-stoppage duration, thereby evaluating an evaluated integrated value of power consumed by the battery during stoppage of an idling. If the integrated value is not less than the evaluated integrated value, the stopping of the engine E is permitted.