A fuel vapor feed controlling apparatus of a lean burn internal combustion engine suppresses either one of a rich misfire or a surge when fuel vapor is fed into the engine. A purge controlling unit controls an amount of fuel vapor fed from a fuel reservoir to the engine in response to an operational condition of the engine. A first compensation unit compensates the amount of fuel vapor such that an engine revolution speed of the engine may be identical with a target revolution speed. The purge controlling unit performs a purge control based on a compensation value compensated by the first compensation unit.