An automatic engine-stop control apparatus for a vehicle includes a vehicle speed sensor and a brake pedal depression sensor which are coupled to a control unit. The control unit is programmed to decide that the vehicle speed detected by the vehicle speed sensor is smaller than or equal to a predetermined stop expected speed when the brake pedal depression sensor detects that the brake pedal is depressed, and to decide that the vehicle is stopped when a predetermined time period elapses from a moment that the vehicle speed becomes smaller than or equal to the predetermined stop expected speed and when the depression of the brake pedal is continued.