A fuel vapor purge system is configured to execute a highly accurate leak diagnosis with respect to a fuel vapor leak. After the engine is stopped, the temperature of the fuel vapor rises temporarily and then decreases until it reaches the outside ambient temperature. During this period, the purge line is closed off and a minimum value reached by the purge line pressure is detected. The difference between the minimum value of the purge line pressure and the atmospheric pressure is compared to a threshold value. The purge system is diagnosed as "normal" if the difference is equal to or larger than the threshold value and a "leaking" if the difference is less than the threshold value.