The spectral reconstruction theory of Fourier-transform imaging spectrometer is based on the Fourier-transform relationship between the spectrum of the source and the interferogram so that the spectral reconstruction can be simply achieved by using Fourier transform or Fourier cosine transform. However, the traditional Fourier transform solution is carried out in the complex-number field and the result is also a complex-number sequence. To acquire the real-number reconstructed spectrum, people usually use the real part or the absolute magnitude of the transformation result as the reconstructed spectrum, which will introduce in an extra-phase to the spectrum and lead to inaccuracy of reconstructed spectral intensity. Although reseachers use Fourier cosine transform to avoid the extra-phase problem effectively, this solution has a boundary condition problem which cannot be avoid and may also lead to inaccuracy of reconstructed spectral intensity. To solve the problem, on the base of the analysis of traditional reconstruction solutions, an improved spectral reconstruction solution based on Fourier conjugate correction (FCC) for Fourier-transform spectrometer is developed and discussed. Firstly the conjugated symmetrical form of the interferogram sequence is created by the use of the original interferogram captured, and then the conjugated symmetrical spectrum and the correction element can be acquired by carrying out Fourier transform to the sequence. By using the conjugated symmetrical spectrum and the correction element, the real-number spectrum sequence can be calculated. By carrying out both the simulation and the experiment using helium lamp, it can be concluded that the FCC solution can avoid either the extra-phase problem caused by discrete Fourier transform (DFT) solution or the boundary condition caused by discrete Fourier cosine transform (DCT) solution effectively and improve the reconstructed spectral intensity accuracy.