In order to enhance the photon flux and brightness of a synchrotron source, and improve the thermal stability of optical elements, synchrotron radiation source often operates in the qusi-constant current injection (Top-Up) mode. The Top-Up mode can maintain a stable beam current in the storage ring of Synchrotron Source. When the electron is injected into the storage ring from the booster, a noise induced by the instantaneous fluctuation of the beam current in the storage ring will cause a large fluctuation on the interferogram, which can be observed by the FTIR spectrometer used in IR experimental endstation. The median filtering algorithm is not sufficient to filter the noise according to the noise characteristics. Therefore, a zone median filter method is proposed to eliminate the noise introduced by the Top-Up mode. A set of the processes of zone median filtering algorithm is designed, which can eliminate the Top-Up mode induced noise on the interferogram automatically. Simulation results show that: the filtering algorithm can be applied to eliminate the noise on the interferogram introduced by the Top-Up mode effectively,so the method can be used to enhance the spectral SNR of the spectrum in the Top-Up mode.