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The stepped micro-mirror imaging Fourier transform spectrometer (SIFTS) has the advantages of high throughput, compactness, and stability. However, the systematic errors in the interference core of the SIFTS have a significant impact on the interferogram and the reconstructed spectrum. In order to reduce the influence of systematic errors, a transfer error model of the systematic errors in the interference core of the SIFTS is established, and an interferogram and spectrum calibration method is presented, which combines the least squares fitting calibration and the row-by-row fast Fourier transform-inverse fast Fourier transform (FFT-IFFT) flat-field calibration. The experimental results show that the methods can sufficiently reduce the influence of systematic errors in the interference core of the SIFTS, such as the interferogram fringe tilt, the peak position shift of the reconstructed spectrum, and the error of spectral response.