A novel apodization function is proposed. The new apodization function multiplied by zerocrossing single sided interferogram can average the product of twiddle factor and intensity of two points having the same optical path difference, and reduce the error due to the data around zero optical path difference used twice. The simulation results show that the new apodization function fits better in some serious unsymmetrical interferograms than the Mertz apodization function and can minish the spectral distortion. Moreover, the computational complexity can be reduced significantly. The new apodization function can be widely applied to zerocrossing single sided interferogram data processing of fourier transform spectrometer.