Spatial heterodyne Raman spectrometer (SHRS) is a new developing spectrometer to detect Raman spectra with many advantages over traditional instruments. Several research teams have demonstrated the detection ability of SHRS by experiments and theoretical estimation. However, there still lack descriptions of the spectral restoration method for SHRS. The article provides a spectral restoration method made of two parts, processing method for raw interferogram and processing method for raw Raman spectrum. In the first part, the article describes the processing methods for one-dimensional and two-dimensional interferograms. Using flatfielding, filling zeroes, Fourier transform and row averaging for one-dimensional SHRS or finding spectral row for two-dimensional SHRS, the raw interferogram achieved by SHRS can be translated to raw Raman spectrum. In another part, the authors provide the spike removal method for raw Raman spectrum. The processing results show that the restoration method has a good performance for the real Raman spectra achieved by an SHRS breadboard. Copyright (c) 2017 John Wiley & Sons, Ltd.