Using a new class of apodization function, the effects of apodization on resolution in FT-IR spectrometer are studied. Results show that the degradation of resolution as a result of apodization does not necessarily occur. Given fine apodization functions, the resolution may be better than that of the unapodized while the largest secondary maximum remains at the same level. Experimental results show that the performances of the instrument could be upgraded if the new apodization functions are applied to FT-IR spectrometer.