An engine stopping and starting system for automatically stopping and starting an engine of a vehicle, said engine including: fuel injection control means for controlling a fuel injection amount and a fuel injection timing in each of a plurality of fuel injection valves adapted to inject fuel directly into a corresponding plurality of cylinders (12A-12D); ignition control means for controlling each ignition timing of a plurality of spark plugs provided in the corresponding cylinders (12A-12D); an alternator designed to be driven by the engine and operable to allow an output current therefrom to be a predetermined target output current; rotational speed detecting means (30, 31) for detecting an engine speed; and intake-air flow-rate adjusting means for adjusting an intake-air flow rate to be supplied to each of the cylinders (12A-12D), said engine stopping/starting system being characterized by comprising: automatic stop control means operable, upon satisfaction of a predetermined automatic engine stop condition, to control said fuel injection valves to interrupt the fuel injection for maintaining an operating state of the engine, so as to automatically stop the engine; and automatic engine start control means operable, upon satisfaction of a restart condition for restarting said automatically stopped engine, to allow the fuel injection valve of at least the cylinder in the state after being automatically stopped in an expansion stroke, to inject fuel into said cylinder, and allow the spark plug of said cylinder to ignite an air-fuel mixture and induce combustion in said cylinder, so as to automatically restart said engine, wherein said automatic stop control means is operable, during said automatic engine stop control, to allow said intake-air flow-rate adjusting means to increase the intake-air flow rate to be supplied to each of the cylinders (12A-12D) when the fuel injection is interrupted, then allow said alternator to increase said target output current to a predetermined initial value, and then reduce said target output current of said alternator to a value less than said initial value depending on the level of lowering in engine speed occurring after the interruption of said fuel injection, and said automatic stop control means is operable, after the increase of said target output current to said initial value, to determine a decrement from said initial value of said target output current in accordance with an engine speed detected by said rotational speed detecting means (30, 31) at a time when an engine crank angle becomes equal to a predetermined detection angle, wherein said decrement is set at a larger value when said detected engine speed has a smaller value. fuel injection control means for controlling a fuel injection amount and a fuel injection timing in each of a plurality of fuel injection valves adapted to inject fuel directly into a corresponding plurality of cylinders (12A-12D); ignition control means for controlling each ignition timing of a plurality of spark plugs provided in the corresponding cylinders (12A-12D); an alternator designed to be driven by the engine and operable to allow an output current therefrom to be a predetermined target output current; rotational speed detecting means (30, 31) for detecting an engine speed; and intake-air flow-rate adjusting means for adjusting an intake-air flow rate to be supplied to each of the cylinders (12A-12D), automatic stop control means operable, upon satisfaction of a predetermined automatic engine stop condition, to control said fuel injection valves to interrupt the fuel injection for maintaining an operating state of the engine, so as to automatically stop the engine; and automatic engine start control means operable, upon satisfaction of a restart condition for restarting said automatically stopped engine, to allow the fuel injection valve of at least the cylinder in the state after being automatically stopped in an expansion stroke, to inject fuel into said cylinder, and allow the spark plug of said cylinder to ignite an air-fuel mixture and induce combustion in said cylinder, so as to automatically restart said engine, wherein said automatic stop control means is operable, during said automatic engine stop control, to allow said intake-air flow-rate adjusting means to increase the intake-air flow rate to be supplied to each of the cylinders (12A-12D) when the fuel injection is interrupted, then allow said alternator to increase said target output current to a predetermined initial value, and then reduce said target output current of said alternator to a value less than said initial value depending on the level of lowering in engine speed occurring after the interruption of said fuel injection, and said automatic stop control means is operable, after the increase of said target output current to said initial value, to determine a decrement from said initial value of said target output current in accordance with an engine speed detected by said rotational speed detecting means (30, 31) at a time when an engine crank angle becomes equal to a predetermined detection angle, wherein said decrement is set at a larger value when said detected engine speed has a smaller value.