Infrared spectra are often corrupted by noise, which may greatly influence the accuracy and precision of the analytical result. To improve the analytical precision, the authors need to denoise the spectrum data first. In the present paper, a spectrum denoising method by the second generation wavelet transform domain thresholding combined with the median filtering is introduced. The spectrum of a certain kind of wheat was used to test the performance of the proposed denoising method. In the experiment, noise with signal to noise ratio 21.17 dB was first added to the spectrum, and then removed by the proposed denoising method. The signal to noise ratio (SNR), the root mean square error(RMSE), the average relative error of the peak value (AREPV) and the average error of the peak position (AEPP) were used to evaluate the performance of the proposed denoising method. Experimental results show that the proposed method can remove the spectrum noise and keep the useful information more effective than Donoho’s soft and hard threshold method. At the same time, it can achieve a higher PSNR, a lower RMSE, a lower AREPV and a lower AEPP than the other two denoising methods.