In this paper, parallel-processing algorithms for spectrum reconstruction in Fourier transform imaging spectroscopy are proposed using high-performance parallel computing. Because of the huge amount of interference data, traditional algorithms are inefficient and time-consuming. It is necessary to process interference data as soon as possible to form spectral data for research and economy. We take advantage of parallel computing based on the graphics processing unit (GPU) to enable higher efficiency and reduced operation time. Furthermore, traditional algorithms for processing interferograms on the central processing unit are introduced for comparison. The experimental results show that the runtime is reduced from 1.144 to 0.332 ms using our parallel algorithms, and for the huge amount of data, the designed parallel-processing mechanism on the GPU has advantages over the traditional pipeline.