PURPOSE: To collect a fuel vapor effectively by controlling the opening/closing of a valve device after the lapse of time sufficient to stop an internal combustion engine perfectly after the turning off of an ignition switch.

CONSTITUTION: It is judged whether a prohibition time sufficient to the perfect stop of an engine lapses from the turning off of an ignition switch 16 and when it down not lapse yet, a solenoid valve 11 is not opened during the rotation of inertia. In other words, such passage for the back flow of a fuel vapor as a canister 13, an outer vent 12, a solenoid valve 11, a float room 3, an inner vent 10 and an intake system 1 is not formed. Consequently, the generation of a run-on by which the rotation of the engine is continued can be prevented surely. Thereafter, the solenoid valve 11 is opened for a prescribed time and the fuel vapor in the float room 3 is adsorbed to the canister 13 surely. Accordingly, it does not flow in the intake system 1 through the inner vent 10 at the restart time and as a mixture does not become overrich, startability can be held favorably.