Phase error correction is one of the key steps in generating high quality spectrum. The commonly used Mertz method that recovers the spectrum from zero-crossing sampled single-sided interferogram data can correct the phase error efficiently. However, this method do not uniformly utilize the asymmetric interferogram data, which causes theinaccuracy of high frequency components in the spectrogram. To address this problem, an improved Mertz-based phase correction method is proposed by weighting asymmetric interferogram with an odd polynomial. The improved Mertz method can utilize the spectral information of small bilateral interferograms uniformly. Extensive experiments demonstrate that the proposed method can effectively recover the spectral details and improve the spectral signal-to-noise ratio. Compared with the method using linear weighting function, the proposed odd polynomial increases the average peak-to-peak signal-to-noise ratio by 1.2% and 2.3%, and improves the root mean square signal-to-noise ratio by 3.6% and 1.1% in 900～1100 cm－1 and 2500～2600 cm－1 bands, respectively.