PURPOSE: To carry out a sure fuel cut-off, by determining that an engine enters once into a decelerating condition, if the vacuum in an intake-air pipe is higher than a set vacuum, and then by determining that the engine is in a substantial decelerating condition, if the intake-air pipe vacuum is lower than a second set vacuum after a predetermined time elapses.

CONSTITUTION: In each of conditions that a water temperature switch 14 is turned on in an engine warm-up condition, an air-conditioning switch is turned off since the air-conditioning switch is not used, a neutral switch 15 is turned on in a certain speed shift position and a clutch switch 16 is turned on in the engaged condition of a clutch, when a vehicles runs at a speed above a set vehicle speed V1, the output of an AND gate 29 becomes a high level, and the output of a comparator 27 also becomes a high level. In this condition the vacuum in an intake-air pipe comes t be high in accordance with the opening of an accelerator. If the vacuum in the intake-pipe exceeds a first set vacuum P1, a timer 25 is set in association with the output of the comparator 21, and if the intake-vacuum is still high after the set time of the timer elapses, it is determined that the engine is in a decelerating range, and a slow-cut solenoid valve 9 is deenergized to cut off fuel.